模块化非线性系统辨识算法研究
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摘要
作为系统和控制科学的核心问题之一,系统辨识在控制系统的设计与分析方面得到了广泛地应用,并且已经深入到了生物学、生理学、医学、社会学等众多的科学技术领域。从而,系统辨识成为目前相当活跃的学科之一,吸引了大量的科技人员对其理论进行研究,探讨在不同实际问题中应用的可能性。
在系统辨识方法研究中,由于工程实际对象的复杂性,使得非线性系统辨识方法在工程对象的分析中表现出明显的优势。然而,因为非线性系统固有的复杂多样性,目前关于非线性的研究还远没有达到成熟的程度,蕴涵在复杂现象背后的“本质问题”还没有完全揭示出来。因此,传统的辨识方法始终未能很好地解决复杂的非线性对象的辨识,非线性系统的辨识一直是当今国际辨识界所关心的问题。
辨识非线性系统的困难之一就是缺乏描述各种非线性系统特性的统一的数学模型。为此,这就需要人们分门别类地去探讨研究,解决所遇到的各种具体问题。因此,本文对模块化非线性系统的辨识算法进行了探讨和研究,期望在实际问题的应用中取得良好效果。论文的具体研究工作如下：
1.利用粒子群优化算法研究了非线性系统的辨识问题。基本思想是：将非线性系统模块化后,给出基于粒子群优化算法的新型辨识方法。即就是说,首先,由典型数学模型相互组合来构成系统模型,将系统结构辨识问题转化为组合优化问题；然后,采用粒子群优化算法对系统的结构与参数进行辨识。利用仿真结果说明了所给的辨识方法是合理的和有效的。
2.针对非线性环节为分段函数的模块化非线性系统,利用关键变量分离的原理,分离出线性环节的关键变量,将非线性环节表达式代入到其中去,使整个系统的输出表示为所有待估参数的回归方程形式。然后,将回归方程信息向量中未知真实输出、未知中间变量和不可测噪声项分别用辅助模型的输出、中间变量估计值和估计残差来代替,将非线性系统的辨识问题转化为参数空间上的函数优化问题。接着,采用粒子群优化算法获得该优化问题的解。最后,进行了仿真研究,其结果验证了所给辨识方法的有效性。
3.研究了由一线性动态子系统和一无记忆的非线性增益串联构成的模块化非线性模型的盲辨识算法问题。当系统输入不采用高斯随机信号时,利用循环平稳输入信号的一阶统计特性和模型非线性部分的逆映射,将有输入信号的系统辨识过程转变为无输入信号的辨识过程,并且利用输出信号恢复了所有的中间变量。然后,通过支持向量机线性回归算法和高阶累积量方法来求取模型的参数。最后,仿真结果表明了所给的盲辨识方法是有效的和稳定的。
4.针对一类多输入单输出的模块化非线性模型,其辨识问题可等价成以待估计参数为优化变量的非线性极小值优化问题。该方法的基本思想是将非线性系统的辨识问题转化为参数空间上的优化问题,然后,采用粒子群优化算法获得该优化问题的解。为了进一步增强粒子群优化算法的辨识性能,提出了利用一种混合粒子群优化算法。最后,通过仿真结果说明所给辨识方法的有效性和实用性。
5.研究了对单输入单输出的采样模块化非线性Hammerstein-Wi ener模型的盲辨识算法问题。当系统输入不采用白噪声信号时,通过盲信号处理方法,仅仅利用输出信号恢复了所有中间变量。然后,通过支持向量机线性回归算法求取了模型的线性部分和非线性部分的参数。最后,在仿真实验中,与使用最小二乘法进行了比较,结果表明了所给的盲辨识方法是切实可行的。
6.为了提高小波神经网络对非线性系统的辨识性能,利用一种改进粒子群优化算法对BP小波神经网络参数进行训练,求得最优值,达到对非线性系统辨识目的。在数值仿真中,与采用标准粒子群优化算法相比,结果显示了所给的方法在收敛性和稳定性等方面均得到了明显地改善。
As one of the key issues of system and control science, system identification has been widely applied to the design and analysis of control system, and has been gone deep into many fields of science and technology, such as biology, physiology, medicine, sociology, and so on. Consequently, system identification becomes one of the current very active subjects, attracting a large number of scientific and technical personnel for their theoretical study to examine the practical problems in different application possibilities.
In research on the method of system identification, because many engineering objects are very complex, the identification methods of nonlinear systems show remarkable advantage in the analysis of the engineering object. However, because of the inherent complexity and diversity of nonlinear systems, the current research on the nonlinear far not reached the degree of maturity; it has not been fully revealed that the "essence problem" of nonlinear was contained behind the complex phenomenon. Thereby, the complex nonlinear object recognitions are still not well solved via the traditional identification methods; the identification of nonlinear system was the main topics in the current international identification fields.
For the identification of nonlinear system, one of the difficulties is short of unified mathematical model to description of various nonlinear system features. To this end, one should study on different specific problems. Consequently, in this paper, the identification algorithms of blocking nonlinear systems are discussed and studied, and expected good results in practical applications. The main research work is as follows:
1. The identification problem of nonlinear system was studied based on a particle swarm optimization algorithm. The basic idea is that identification method was given by a particle swarm optimization algorithm, after the nonlinear system was blocked. That is to say, first of all, the idea of the method employed a system model composed with classical models so as to transform the system structure identification problem into a combinational problem. And then, a particle swarm optimization algorithm was adopted to implement the identification on the system structure and parameters. Simulation results showed the rationality and effectiveness of the presented method.
2. The parameter identification method of blocking nonlinear model with two-segment piecewise nonlinearities was presented. Its basic idea is that:Firstly, expressing the output of the blocking nonlinear models as a regressive equation in all parameters based on the key term separation principle and separating key term from linear block and nonlinear block. Secondly, the unknown true outputs of the information vector are replaced with the outputs of an auxiliary model; the unknown internal variables and the unmeasured noise terms are replaced with the estimated internal variables and the estimated residuals, respectively. Accordingly, the problem of nonlinear system identification was cast as function optimization over parameter space, and then, a particle swarm optimization algorithm was adopted to solve the optimization problem. Finally, simulation results showed the effectiveness of the proposed method.
3. A blind identification algorithm to a blocking nonlinear model, where the nonlinear block is a linear subsystem is followed by a memoryless nonlinear gain, was investigated. When the input signal of system didn't adopt a Gaussian random signal, the identification process with the input signal was changed into the one without input signal using the first-order moment of the cyclostationary input signal and the inverse nonlinear mapping of the nonlinear model. And all internal variables were recovered based on the output signal. Then, parameters of the model were obtained through support vector machine linear regression algorithm and higher order cumulants method. Finally, the efficiency and stability of the presented algorithm were demonstrated by simulation examples.
4. For a class of multi-input single-output blocking nonlinear model, the model identification problem is equivalent to the nonlinear minimization problem with the estimated parameters as the optimized variables. The basic idea of the method is that the problem of the nonlinear system identification was changed into an optimization problem in parameter space and a particle swarm optimization algorithm was then adopted to solve the optimization problem. In order to enhance the identification performance of the particle swarm optimization algorithm, a hybrid particle swarm optimization algorithm was also adopted. Finally, simulation results showed the effectiveness and practicality of the proposed identification method.
5. A blind identification algorithm for the single-input single-output sampled blocking nonlinear Hammerstein-Wiener model was proposed. When the input signal of the system didn't adopt a white noise signal, by a blind signal disposal approach, all internal variables were recovered solely based on the output signal. Then, parameters of linear and nonlinear parts of the model were obtained through support vector machine linear regression algorithm. Finally, in simulation experiments, compared with using least square method, the effectiveness of the presented algorithm was illustrated.
6. In order to improve the identification performance of the wavelet neural network for the nonlinear system, the parameters of a BP wavelet neural network were trained via an improved particle swarm optimization algorithm to obtain optimal values to achieve the purpose of identification for the nonlinear system. In numerical simulation, compared with using standard particle swarm optimization algorithm, the results showed that the presented algorithm was obviously improved in the convergence, stability, and so on.
在系统辨识方法研究中,由于工程实际对象的复杂性,使得非线性系统辨识方法在工程对象的分析中表现出明显的优势。然而,因为非线性系统固有的复杂多样性,目前关于非线性的研究还远没有达到成熟的程度,蕴涵在复杂现象背后的“本质问题”还没有完全揭示出来。因此,传统的辨识方法始终未能很好地解决复杂的非线性对象的辨识,非线性系统的辨识一直是当今国际辨识界所关心的问题。
辨识非线性系统的困难之一就是缺乏描述各种非线性系统特性的统一的数学模型。为此,这就需要人们分门别类地去探讨研究,解决所遇到的各种具体问题。因此,本文对模块化非线性系统的辨识算法进行了探讨和研究,期望在实际问题的应用中取得良好效果。论文的具体研究工作如下：
1.利用粒子群优化算法研究了非线性系统的辨识问题。基本思想是：将非线性系统模块化后,给出基于粒子群优化算法的新型辨识方法。即就是说,首先,由典型数学模型相互组合来构成系统模型,将系统结构辨识问题转化为组合优化问题；然后,采用粒子群优化算法对系统的结构与参数进行辨识。利用仿真结果说明了所给的辨识方法是合理的和有效的。
2.针对非线性环节为分段函数的模块化非线性系统,利用关键变量分离的原理,分离出线性环节的关键变量,将非线性环节表达式代入到其中去,使整个系统的输出表示为所有待估参数的回归方程形式。然后,将回归方程信息向量中未知真实输出、未知中间变量和不可测噪声项分别用辅助模型的输出、中间变量估计值和估计残差来代替,将非线性系统的辨识问题转化为参数空间上的函数优化问题。接着,采用粒子群优化算法获得该优化问题的解。最后,进行了仿真研究,其结果验证了所给辨识方法的有效性。
3.研究了由一线性动态子系统和一无记忆的非线性增益串联构成的模块化非线性模型的盲辨识算法问题。当系统输入不采用高斯随机信号时,利用循环平稳输入信号的一阶统计特性和模型非线性部分的逆映射,将有输入信号的系统辨识过程转变为无输入信号的辨识过程,并且利用输出信号恢复了所有的中间变量。然后,通过支持向量机线性回归算法和高阶累积量方法来求取模型的参数。最后,仿真结果表明了所给的盲辨识方法是有效的和稳定的。
4.针对一类多输入单输出的模块化非线性模型,其辨识问题可等价成以待估计参数为优化变量的非线性极小值优化问题。该方法的基本思想是将非线性系统的辨识问题转化为参数空间上的优化问题,然后,采用粒子群优化算法获得该优化问题的解。为了进一步增强粒子群优化算法的辨识性能,提出了利用一种混合粒子群优化算法。最后,通过仿真结果说明所给辨识方法的有效性和实用性。
5.研究了对单输入单输出的采样模块化非线性Hammerstein-Wi ener模型的盲辨识算法问题。当系统输入不采用白噪声信号时,通过盲信号处理方法,仅仅利用输出信号恢复了所有中间变量。然后,通过支持向量机线性回归算法求取了模型的线性部分和非线性部分的参数。最后,在仿真实验中,与使用最小二乘法进行了比较,结果表明了所给的盲辨识方法是切实可行的。
6.为了提高小波神经网络对非线性系统的辨识性能,利用一种改进粒子群优化算法对BP小波神经网络参数进行训练,求得最优值,达到对非线性系统辨识目的。在数值仿真中,与采用标准粒子群优化算法相比,结果显示了所给的方法在收敛性和稳定性等方面均得到了明显地改善。
As one of the key issues of system and control science, system identification has been widely applied to the design and analysis of control system, and has been gone deep into many fields of science and technology, such as biology, physiology, medicine, sociology, and so on. Consequently, system identification becomes one of the current very active subjects, attracting a large number of scientific and technical personnel for their theoretical study to examine the practical problems in different application possibilities.
In research on the method of system identification, because many engineering objects are very complex, the identification methods of nonlinear systems show remarkable advantage in the analysis of the engineering object. However, because of the inherent complexity and diversity of nonlinear systems, the current research on the nonlinear far not reached the degree of maturity; it has not been fully revealed that the "essence problem" of nonlinear was contained behind the complex phenomenon. Thereby, the complex nonlinear object recognitions are still not well solved via the traditional identification methods; the identification of nonlinear system was the main topics in the current international identification fields.
For the identification of nonlinear system, one of the difficulties is short of unified mathematical model to description of various nonlinear system features. To this end, one should study on different specific problems. Consequently, in this paper, the identification algorithms of blocking nonlinear systems are discussed and studied, and expected good results in practical applications. The main research work is as follows:
1. The identification problem of nonlinear system was studied based on a particle swarm optimization algorithm. The basic idea is that identification method was given by a particle swarm optimization algorithm, after the nonlinear system was blocked. That is to say, first of all, the idea of the method employed a system model composed with classical models so as to transform the system structure identification problem into a combinational problem. And then, a particle swarm optimization algorithm was adopted to implement the identification on the system structure and parameters. Simulation results showed the rationality and effectiveness of the presented method.
2. The parameter identification method of blocking nonlinear model with two-segment piecewise nonlinearities was presented. Its basic idea is that:Firstly, expressing the output of the blocking nonlinear models as a regressive equation in all parameters based on the key term separation principle and separating key term from linear block and nonlinear block. Secondly, the unknown true outputs of the information vector are replaced with the outputs of an auxiliary model; the unknown internal variables and the unmeasured noise terms are replaced with the estimated internal variables and the estimated residuals, respectively. Accordingly, the problem of nonlinear system identification was cast as function optimization over parameter space, and then, a particle swarm optimization algorithm was adopted to solve the optimization problem. Finally, simulation results showed the effectiveness of the proposed method.
3. A blind identification algorithm to a blocking nonlinear model, where the nonlinear block is a linear subsystem is followed by a memoryless nonlinear gain, was investigated. When the input signal of system didn't adopt a Gaussian random signal, the identification process with the input signal was changed into the one without input signal using the first-order moment of the cyclostationary input signal and the inverse nonlinear mapping of the nonlinear model. And all internal variables were recovered based on the output signal. Then, parameters of the model were obtained through support vector machine linear regression algorithm and higher order cumulants method. Finally, the efficiency and stability of the presented algorithm were demonstrated by simulation examples.
4. For a class of multi-input single-output blocking nonlinear model, the model identification problem is equivalent to the nonlinear minimization problem with the estimated parameters as the optimized variables. The basic idea of the method is that the problem of the nonlinear system identification was changed into an optimization problem in parameter space and a particle swarm optimization algorithm was then adopted to solve the optimization problem. In order to enhance the identification performance of the particle swarm optimization algorithm, a hybrid particle swarm optimization algorithm was also adopted. Finally, simulation results showed the effectiveness and practicality of the proposed identification method.
5. A blind identification algorithm for the single-input single-output sampled blocking nonlinear Hammerstein-Wiener model was proposed. When the input signal of the system didn't adopt a white noise signal, by a blind signal disposal approach, all internal variables were recovered solely based on the output signal. Then, parameters of linear and nonlinear parts of the model were obtained through support vector machine linear regression algorithm. Finally, in simulation experiments, compared with using least square method, the effectiveness of the presented algorithm was illustrated.
6. In order to improve the identification performance of the wavelet neural network for the nonlinear system, the parameters of a BP wavelet neural network were trained via an improved particle swarm optimization algorithm to obtain optimal values to achieve the purpose of identification for the nonlinear system. In numerical simulation, compared with using standard particle swarm optimization algorithm, the results showed that the presented algorithm was obviously improved in the convergence, stability, and so on.
引文
[1]Ljung L. System identification:theory for the user [M].2nd ed. Englewood Cliffs, NJ:Prentice Hall, 1999.
[2]方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1988.
[3]朱豫才.著.张湘平,虞水俊,孙志强,胡德文.译.过程控制的多变量系统辨识[M].长沙：国防科技大学出版社,2004.
[4]吴广玉.系统辨识与自适应[M].哈尔滨：哈尔滨工业大学出版社,1987.
[5]刘福才.非线性系统的模糊模型辨识及其应用[M].北京：国防工业出版社,2006.
[6]侯媛彬,汪梅,王立琦.系统辨识及其MATLAB仿真[M].北京：科学出版社,2004.
[7]朱全民.非线性系统辨识[J].控制理论与应用,1994,11(6)：641-652.
[8]Giannakis G B, Serpedin E. A bibliography on nonlinear system identification [J]. Signal Processing, 2001,81(3):533-580.
[9]Billings S A. Identification of nonlinear systems—a survey [J]. IEE Proceedings,1980,6:272-285.
[10]Sjoberg J, Zhang Q H, Ljung L, Benveniste A, Deylon B, Glorennec P Y, Hjalmarsson H, Juditsky A. Nonlinear black-box modeling in system identification:a unified overview [J]. Automatica,1995, 31(12):1691-1724.
[11]Juditsky A, Hjalmarsson H, Benveniste A, Deylon B, Ljung L, Sjoberg J, Zhang Q H. Nonlinear black-box models in system identification:mathematical foundations [J]. Automatica,1995,31(12): 1725-1750.
[12]Vajk I, Hetthessy J. Identification of nonlinear errors-in-variables models [J]. Automatica,2003,39(12): 2099-2107.
[13]Schoukens J, Nemeth J G, Crama P, Rolain Y, Pintelon R. Fast approximate identification of nonlinear systems [J]. Automatica,2003,39(7):1267-1274.
[14]Pia Saccomani M, Audoly S, D'Angio L. Parameter identifiability of nonlinear systems:the role of initial conditions [J]. Automatica,2003,39(4):619-632.
[15]Denis-Vidal L, Joly-Blanchard G. Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems [J]. Automatica,2004,40(2):287-292.
[16]Roll J, Nazin A, Ljung L. Nonlinear system identification via direct weight optimization [J]. Automatica,2005,41(3):475-490.
[17]M kil P M. LTI modelling of NFIR systems:near-linearity and control, LS estimation and linearization [J]. Automatica,2005,41(1):29-41.
[18]M kil P M. On robustness in control and LTI identification:Near-linearity and non-conic uncertainty [J]. Automatica,2006,42(4):601-612.
[19]Wigren T. Recursive prediction error identification and scaling of non-linear state space model using a restricted black box parameterization [J]. Automatica,2006,42(1):159-168.
[20]Anderson S R, Kadirkamanathan V. Modelling and identification of non-linear deterministic systems in the delta-domain [J]. Automatica,2007,43(11):1859-1868.
[21]Bravo J M, Alamo T, Redondo M J, Camacho E F. An algorithm for bounded-error identification of nonlinear systems based on DC functions [J]. Automatica,2008,44(2):437-444.
[22]Yang Z Y, Chan C W. Simultaneous estimation of the input and output frequencies of nonlinear systems [J]. Automatica,2008,44(7):1822-1830.
[23]Xia X, Moog C H. Identifiability of nonlinear systems with application to HIV/AIDS models [J]. IEEE Transactions on Automatic Control,2003,48(2):330-336.
[24]Cao C Y, Annaswamy A M, Kojic A. Parameter convergence in nonlinearly parameterized systems [J]. IEEE Transactions on Automatic Control,2003,48(3):397-412.
[25]Barker H A, Tan A H, Godfrey K R. Optimal levels of perturbation signals for nonlinear systems identification [J]. IEEE Transactions on Automatic Control,2004,49(8):1404-1407.
[26]Li K, Peng J X, Irwin G W. A fast nonlinear model identification method [J]. IEEE Transactions on Automatic Control,2005,50(8):1211-1216.
[27]Espinoza M, Suykens J A K, De Moor B. Kernel based partially linear models and nonlinear identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1602-1606.
[28]Bemporad A, Garulli A, Paoletti S, Vicino A. A bounded-error approach to piecewise affine system identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1567-1580.
[29]Shaw S R, Laughman C R. A method for nonlinear least squares with structured residuals [J]. IEEE Transactions on Automatic Control,2006,51(10):1704-1708.
[30]Zhang J, Xia X, Moog C H. Parameter identifiability of nonlinear systems with time-delay [J]. IEEE Transactions on Automatic Control,2006,51(2):371-375.
[31]Tyukin I Y, Prokhorov D V, Van Leeuwen C. Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parameterization [J]. IEEE Transactions on Automatic Control, 2007,52(9):1543-1559.
[32]Dalai M, Weyer E, Campi M C. Parameter identification for nonlinear systems:guaranteed confidence regions through LSCR [J]. Automatica,2007,43(8):1418-1425.
[33]Bai E W, Liu Y. Recursive direct weight optimization in nonlinear system identification:a minimal probability approach [J]. IEEE Transactions on Automatic Control,2007,52(7):1218-1231.
[34]Li K, Peng J X, Bai E W. A two-stage algorithm for identification of nonlinear dynamic systems [J]. Automatica,2006,42(7):1189-1197.
[35]Bai E W. Identification of nonlinear additive FIR systems [J]. Automatica,2005,41(7):1247-1253.
[36]李言俊,张科.系统辨识理论及应用[M].北京：国防工业出版社,2003.
[37]衷路生.线性系统的迭代优化与子空间辨识方法研究[D].杭州：浙江大学,2007.
[38]Gevers M. A personal view of the development of system identification:a 30-year journey through an
exciting field [J]. IEEE Control Systems Magazine,2006,26(6):93-105.
[39]Astrom K J, Bohlin T. Numerical identification of linear dynamic systems from normal operating records [C]. In Proceedings of IFAC Symposium on Self-Adaptive Systems, England, Teddington, 1965.
[40]Box G E P, Jenkins G M. Time series analysis, forecasting and control [M]. Oakland, CA:Holden-Day, 1970.
[41]Ljung L. Asymptotic variance expressions for identified black-box transfer function models [J]. IEEE Transactions on Automatic Control,1985, AC-30:834-844.
[42]Ljung L. Development of system identification [C]. In Proceedings of 13th World Congress of IFAC, San Francisco, California,1996, G:141-146.
[43]冯培悌.系统辨识[M].杭州：浙江大学出版社,1999.
[44]柯晶.强跟踪状态估计与群集辨识[D].杭州：浙江大学,2003.
[45]窦立谦,宗群,刘文静.面向控制的系统辨识研究进展[J].系统工程与电子技术,2009,31(1)：158-164.
[46]吴旭光.不确定性系统的鲁棒辨识及其发展[J].控制与决策,1996,11(增刊1)：113-118.
[47]冯旭,孙优贤.鲁棒辨识问题评述[J].控制理论与应用,1993,10(6)：609-616.
[48]莫建林,张卫东,许晓鸣.鲁棒辨识研究的现状[J].控制与决策,2002,17(3)：257-263.
[49]Ljung L, Glover K. Frequency domain versus time domain methods in system identification [J]. Automatica,1981,17(1):71-86.
[50]Mckelvey T, Akcay H, Ljung L. Subspace based on multivariable system identification from frequency response data [J]. IEEE Transactions on Automatic Control,1996,41(7):960-979.
[51]Pintelon R. Frequency domain subspace system identification using non-parametric noise models [J]. Automatica,2002,38(3):1295-1311.
[52]Yang Z J, Sanada S. Frequency domain subspace identification with the aid of the w-operator [J]. Electrical Engineering in Japan,2000,132(1):46-56.
[53]Wills A, Ninnes B, Gibson S. Maximum likelihood estimation of state space models from frequency domain data [J]. IEEE Transactions on Automatic Control,2009,54(1):19-33.
[54]Gillberg J, ljung L. Frequency-domain identification of continues-time ARMA models from sampled data [J]. Automatica,2009,45(6):1371-1378.
[55]Sabri K, El Badaoui M, Guillet F, Adib A, Aboutajdine D. A frequency domain-based approach for blind MIMO system identification using second-order cyclic statistics [J]. Signal Processing,2009, 89(1):77-86.
[56]Trnka P, Havlena V. Subspace like identification incorporating prior information [J]. Automatica,2009, 45(4):1086-1091.
[57]Felici F, Van Wingerden J W, Verhaegen M. Subspace identification of MIMO LPV systems using a
periodic scheduling sequence [J]. Automatica,2007,43(10):1684-1697.
[58]Van Wingerden J W, Verhaegen M. Subspace identification of bilinear and LPV systems for open-and closed-loop data [J]. Automatica,2009,45(2):372-381.
[59]Forssell U, Ljung L. Closed-loop identification revisited [J]. Automatica,1999,35(4):1295-1311.
[60]Miskovic L, Karimi A, Bonvin D, Gevers M. Closed-loop identification of multivariable systems:with or without excitation of all references [J]. Automatica,2008,44(8):2048-2056.
[61]Vanden HPM, Schrama R J P. Identification and control closed-loop issues [J]:Automatica,1995, 31(12):1751-1770.
[62]Qin S J, Lin W, Ljung L. A novel subspace identification approach with enforced causal models [J]. Automatica,2005,41(12):2043-2053.
[63]Chiuso A, Picci G. Consistency analysis of some closed-loop subspace identification methods [J]. Automatica,2005,41(2):377-391.
[64]Niedzwiecki M. On the lower smoothing bound in identification of time-varying systems [J]. Automatica,2008,44(2):459-464.
[65]Niedzwiecki M. Optimal and suboptimal smoothing algorithms for identification of time-varying systems with randomly drifting parameters [J]. Automatica,2008,44(7):1718-1727.
[66]Niedzwiecki M. On "cheap smoothing" opportunities in identification of time-varying systems [J]. Automatica,2008,44(5):1191-1200.
[67]Pillonetto G. Identification of time-varying systems in reproducing kernel Hilbert spaces [J]. IEEE Transactions on Automatic Control,2008,53(9):2202-2209.
[68]Pereira da Silva P S, Batista S. On state representation of time-varying nonlinear systems [J]. Automatica,2009,45(5):1260-1264.
[69]戴汝为,周等勇.智能控制与适应性[C].第三届全球智能控制与自动化大会,安徽,合肥,2001：11-17.
[70]王行愚.系统辨识的若干新动向[J].控制理论与应用,1992,9(3)：319-321.
[71]胡德文.非线性与多变量系统相关辨识[M].长沙：国防科技大学出版社,2001.
[72]Volterra V. Theory of functions [M]. Elackie, London,1930.
[73]Suleiman W, Monin A. New method for identifying finite degree Volterra series [J]. Automatica,2008, 44(2):488-497.
[74]金哲,宋执环,何加铭.基于简化Volterra级数的射频功率放大器建模与辨识[J].电路与系统学报,2008,13(5)：90-94.
[75]王文正,何开锋,欧文,韩崇昭.基于Volterra泛函级数的非线性系统的鲁棒辨识[J].控制理论与应用,2003,20(3)：432-436.
[76]欧文,韩崇昭,王文正.Volterra泛函级数在非线性系统辨识中的应用[J].控制与决策,2002,17(2)：239-242.
[77]魏瑞轩,韩崇昭.一种基于Volterra模型的非线性系统具有全解耦结构的递阶式自适应辨识方法[J].控制理论与应用,2002,19(2)：313-316.
[78]习毅,潘丰.基于Hammerstein模型的非线性自适应预测函数控制[J].系统工程与电子技术,2008,30(11)：2237-2240.
[79]丁宝苍,李少远.具有约束的Hammerstein非线性控制系统的设计与分析[J].控制与决策,2003,18(1)：24-28.
[80]Haddad W M, Chellaboina V S. Nonlinear control of Hammerstein systems with passive nonlinear dynamics [J]. IEEE Transactions on Automatic Control,2001,46(10):1630-1634.
[81]Yoshitani N, Hasegawa A. Model-based control of strip temperature for the heating furnace in continuous annealing [J]. IEEE Transactions on Control Systems Technology,1998,6(2):146-156.
[82]苏成利,王树青.一种基于Wiener模型的非线性预测控制算法[J].信息与控制,2007,36(1)：86-92.
[83]邓自立,李春波.自校正解耦信息融合Wiener状态预报器[J].系统工程与电子技术,2007,29(5)：805-809.
[84]田彦涛,徐明,陆佑方,陈关荣.基于Wiener模型的混沌系统辨识研究[J].控制与决策,2003,18(1)：24-28.
[85]Narendra K S, Gallman P G. An iterative method for the identification of nonlinear systems using a Hammerstein model [J]. IEEE Transactions on Automatic Control,1966, AC-11:546-550.
[86]Voros J. Parameter identification of discontinuous Hammerstein systems [J]. Automatica,1997,33(6): 1141-1146.
[87]Chang F, Luus R. A noniterative method for identification using Hammerstein model [J]. IEEE Transactions on Automatic Control,1971, AC-16:464-468.
[88]Pawlak M. On the series expansion approach to the identification of Hammerstein systems [J]. IEEE Transactions on Automatic Control,1991,36(6):763-767.
[89]Bai E W. Identification of systems with hard input nonlinearities [C]. In Perspectives in Control, Moheimani R, Ed. New York:Springer Verlag,2001.
[90]Bai E W, Fu M Y. A blind approach to Hammerstein model identification [J]. IEEE Transactions on Signal Processing,2002,50(7):1610-1619.
[91]Bai E W. Frequency domain identification of Hammerstein models [J]. IEEE Transactions on Automatic Control,2003,48(4):530-542.
[92]Vaurent L, Pintelon R, Schoukens J. Blind maximum likelihood identification of Hammerstein systems [J]. Automatica,2008,44(12):3139-3146.
[93]Goethals M I, Pelckmans K, Suykens J A K, De Moor B. Subspace identification of Hammerstein systems using least squares support vector machines [J]. IEEE Transactions on Automatic Control,2005, 50(10):1509-1519.
[94]Greblicki W. Continuous-time Hammerstein system identification from sampled data [J]. IEEE Transactions on Automatic Control,2006,51(7):1195-1200.
[95]黄正良,万百五,韩崇昭.辨识Hammerstein模型的两步法[J].控制理论与应用,1995,12(1)：34-39.
[96]徐桥南,袁振东.Hammerstein系统参数的集员辨识[J].控制理论与应用,1994,11(2)：211-215.
[97]孔金生,万百五.一种多输入单输出Hammerstein系统的集成辨识方法[J].控制理论与应用,2005,22(4)：517-519.
[98]张广莹,邓正隆.基于Adaline的双线性Hammerstein模型在线参数辨识[J].电机与控制学报,2003,7(3)：222-225.
[99]Sznaier M. Computational complexity analysis of set membership identification of Hammerstein and Wiener systems [J]. Automatica,2009,45(3):701-705.
[100]Chen H F. Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block [J]. IEEE Transactions on Automatic Control,2005,50(10): 1612-1617.
[101]Bai E W, Li D. Convergence of the iterative Hammerstein system identification algorithm [J]. IEEE Transactions on Automatic Control,2004,49(11):1929-1940.
[102]Hjalmarsson H, Gunnarsson S, Gevers M. Optimality and suboptimality of iterative identification and control design schemes [C]. In Proceedings of the American Control Conference,1995,4:2559-2563.
[103]Raich R, Zhou G T, Viberg M. Subspace based approaches for Wiener system identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1629-1634.
[104]Greblicki W. Nonparametric identification of Wiener systems [J]. IEEE Transactions on Information Theory,1992,38(10):1487-1493.
[105]Bai E W, Reyland Jr J. Towards identification of Wiener the least amount of a priori information on the nonlinearity [J]. Automatica,2008,44(4):910-919.
[106]Cerone V, Regruto D. Parameter bounds evaluation of Wiener models with noninvertible polynomial nonlinearities [J]. Automatica,2006,42(10):1775-1781.
[107]Sznaier M, Ma W J, Camps O I, Lim H. Risk adjusted set membership identification of Wiener systems [J]. IEEE Transactions on Automatic Control,2009,54(5):1147-1152.
[108]Hagenblad A, Ljung L, Wills A. Maximum likelihood of Wiener models [J]. Automatica,2008,44(11): 2697-2705.
[109]Giri F, Rochdi Y, Chaoui F Z. An analytic geometry approach to Wiener system frequency identification [J]. IEEE Transactions on Automatic Control,2009,54(4):683-696.
[110]黄正良,吴坚,万百五.辨识Wiener模型的一种新方法[J].控制理论与应用,1996,13(3)：326-332.
[111]李世华,吴福保,李奇.一种基于动态人工神经网络的Wiener模型辨识[J].控制理论与应用, 2000,17(1)：92-95.
[112]张广莹,邓正隆.基于小波分析的非线性系统Wiener模型辨识[J].电机与控制学报,2001,5(2)：95-97,128.
[113]许自豪,李嗣福,陈宗海.基于Lag-SBP的Wiener型非线性系统的辨识方法[J].系统仿真学报,2002,14(8)：1053-1055.
[114]黄毅卿,陈翰馥.子系统为ARMA和分段线性函数的Wiener系统的参数辨识[J].应用数学学报,2008,31(6)：961-980.
[115]Boutayeb M, Darouach M. Recursive identification method for MISO Wiener-Hammerstein model [J]. IEEE Transactions on Automatic Control,1995,40(2):287-291.
[116]Bershad N J, Bouchired S, Castanie F. Stochastic analysis of adaptive gradient identification of Wiener-Hammerstein systems for Gaussian inputs [J]. IEEE Transactions on Signal Processing,2000, 48(2):557-560.
[117]柯晶,姜静,乔谊正.应用混合进化策略辨识Wiener-Hammerstain模型[J].系统工程与电子技术,2006,28(7)：1055-1063.
[118]Bai E-W. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems [J]. Automatica,1998,34(3):333-338.
[119]Zhu Y C. Estimation of an N-L-N Hammerstein-Wiener model [J]. Automatica,2002,38(9): 1607-1614.
[120]Crama P, Schoukens J. Hammerstein-Wiener system estimator initialization [J]. Automatica,2004, 40(9):1543-1550.
[121]Park H C, Sung S W, Lee J. Modeling of Hammerstein-Wiener processes with special input test signals [J]. Industrial & Engineering Chemistry Research,2006,45(3):1029-1038.
[122]桂卫华,宋海英,阳春华.Hammerstein-Wiener模型最小二乘向量机辨识及其应用[J].控制理论与应用,2008,25(3)：393-397.
[123]朱燕飞,谭洪舟,章云.一类非线性系统盲辨识算法及其仿真研究[J].系统仿真学报,2008,20(4)：3782-3784.
[124]Bai E W. A blind approach to the Hammerstein-Wiener model identification [J]. Automatica,2002, 38(6):967-979.
[125]Ninness B, Goodwin G C. Estimation of models quality [J]. Automatica,1995,31(1):32-74.
[126]Gevers M. Identification for control [C]. Plenary lecture at the 5th IFAC Symposium on Adaptive Control and Signal Processing, Budapest,1995:1-12.
[127]Gevers M. Identification for control:from the early achievements to the revival of experiment design [J]. European Journal of Control,2005,11(1):1-18.
[128]Milanese M, Taragna M. H∞set membership identification:a survey [J]. Automatica,2005,41(12): 2019-2023.
[129]Hjalmarsson H. From experiment design to closed-loop control [J]. Automatica,2005,41(3):393-438.
[130]Gevers M. Identification for control [J]. Annual Reviews in Control,1998,22(3):95-106.
[131]Gevers M, Ljung L. Optimal experiment designs with respect to the extended model application [J]. Automatica,1986,22(2):543-554.
[132]Hjalmarsson H, Gevers M, De Bruyn F, Leblond J. Identification for control:closing the loop gives more accurate controllers [C]. In Proceedings of IEEE Conference Decision and Control, Orlando, Florida,1994:4150-4155.
[133]Gevers M. Connecting identification and robust control:a new challenge [C]. In 9th IFAC/IFORS Symposium on identification and system parameter estimation, Hungary,1991:123-134.
[134]柴天佑.鲁棒辨识方法研究[J].控制理论与应用,1999,16(1)：47-51.
[135]Chen J, Gu G, Nett C N. Worst case identification of continuous time systems via interpolation [J]. Automatica,1994,30(12):1825-1837.
[136]李异平.l1鲁棒辨识：最小二乘算法及试验设计[J].控制理论与应用,2003,20(4)：492-502.
[137]Chen J. Frequency domain tests for validation of linear fractional uncertain models [J]. IEEE Transactions on Automatic Control,1997,42(6):748-760.
[138]Parrilo P A, Sznaier M. Mixed time/frequency-domain based robust identification [J]. Automatica, 1998,34(11):1375-1389.
[139]Bitmead R, Zang Z. An iterative identification and control strategy [C]. In Proceedings of European Control Conference, Grenoble,1991:1395-1400.
[140]Callafon D, Van Den Hof P. Suboptimal feedback control by a scheme of iterative identification and control design [J]. Mathematical Modelling of Systems,1997,3(10):77-101.
[141]Anderson B D O, Bombois X, Gevers M. Caution in iterative modeling and control design [C]. In Proceedings of the IFAC Conference on Adaptive Systems in Control and Signal Processing, Glasgow, U.K.,1998:13-19.
[142]Holmberg U, Valentinotti S, Bonvin D. An identification for control procedure with robust performance [J]. Control Engineering Practice,2000,8(10):1107-1117.
[143]Akcay H, Heuberger P. A frequency-domain iterative identification algorithm using general orthonormal basis functions [J]. Automatica,2001,37(5):663-674.
[144]Date P, Lanzon A. A combined iterative scheme for identification and control redesigns [J]. International Journal of Adaptive Control and Signal Processing,2004,18(8):629-644.
[145]Hildebrand R, Lecchini A, Solari G, et al. Prefiltering in iterative feedback tuning:optimization of the prefilter for accuracy [J]. IEEE Transactions on Automatic Control,2004,49(10):1801-1805.
[146]Viberg M. Subspace-based methods for the identification of linear time invariant systems [J]. Automatica,1995,31(12):1835-1851.
[147]Favoreel W, De Moor B, Van Overschee P. Subspace state space system identification for industrial processes[J]. Process Control,2000,10(2-3):149-155.
[148]Astrom K J, Eykhoff P. System identification-a survey [J]. Automatica,1971,7(1):123-167.
[149]Box G E, Jenkins G M. Time series analysis, forecasting and control, holden-day series in time series analysis and digital processing [M]. Holden-Day, Oacland, Revised Edition,1976.
[150]Eykhoff P. System identification [M]. Wiley, London,1974.
[151]Goodwin G C, Payne R L. Dynamic system identification:experiments design and data analysis [M]. N. Y., Academic Press 1977.
[152]夏天昌.系统辨识—最小二乘法[M].北京：国防工业出版社,1984.
[153]Kung S Y. A new identification method and reduction algorithm via singular value decomposion [C]. In 12th Asilomar Conference on Circuits and Systems, CA,1978.
[154]Lew J S, Juang N, Longman R W. Comparision of several system identification methods for flexible structures [J]. Journal of Vibration,1993,167(2):461-480.
[155]Moonen M, De Moor B,et al. On-line and off-line identification of linear state space models [J]. International Journal of Control,1989,49(1):219-232.
[156]Arun K S, Kung S Y. Balanced approximation of stochastic system [J]. SIAM Journal of Matrix Analysis and Application,1990,11(1):42-68.
[157]Westwick D, Verhaegen M. Identifying MIMO Wiener systems using subspace model identification methods [J]. Signal Processing,1996,52(2):235-258.
[158]Verhaegen M, Westwick D. Identifying MIMO Hammerstein systems in the context of subspace model identification methods [J]. International Journal of Control,1996,63(2):331-349.
[159]Verhaegen M, Yu X D. A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems [J]. Automatica,1995,31(2):201-216.
[160]Verdult V, Verhaegen M. Subspace identification of multivariable linear parameter-varying systems [J]. Automatica,2002,38(5):805-814.
[161]Van Overschee P, De Moor B. Continuous-time frequency domain subspace system identification [J]. Signal Processing,1996,52(2):179-194.
[162]Ohsumi A, Kameyama K, Yamaguchi K I. Subspace identification for continuous-time stochastic systems via distribution-based approach [J]. Automatica,2002,38(1):63-79.
[163]Ljung L, Gunnarsson S. Adaptation and tracking in system identification [J]. Automatica,1990,26(1): 7-21.
[164]Maciej N. Identification of time-varying processes [M]. New York:Wiley,2000.
[165]何振亚.自适应信号处理[M].北京：科学出版社,2002.
[166]Sun Z X, Zhang Z, Tsao T C. Trajectory tracking and disturbance rejection for linear time-varying system:input/output representation [J]. Systems & Control Letters,2009,58 (6):452-460.
[167]Joensen A, Madsen H, Nielsen H A, Nielsen T S. Tracking time-varying parameters with local regression [J]. Automatica,2000,36 (8):1199-1204.
[168]Zhou Q G, Cluett W R. Recursive identification of time-varying systems via incremental estimation [J]. Automatica,1996,32 (10):1427-1431.
[169]Bai E W, Huang Y F. Variable gain parameter estimation algorithms for fast tracking and smooth steady state [J]. Automatica,2000,36 (7):1001-1008.
[170]Lozano R, Dimogianopoulos D, Mahony R. Identification of linear time-varying systems using a modified least-squares algorithm [J]. Automatica,2000,36 (7):1009-1015.
[171]Xue Y C, Qian J X. A modified recursive least squares algorithm with variable parameters and resetting for time-varying system [J]. Chinese Journal of Chemical Engineering,2002,10 (3):298-303.
[172]Sandberg H. A case study in model reduction of linear time-varying systems [J]. Automatica,2006,42 (7):467-472.
[173]Xu J X, Pan Y J, Lee T H. A VSS identification.scheme for time-varying parameters [J]., Automatica, 2003,39 (4):727-734.
[174]Young P. Parameter estimation for continuous-time models:a survey [J]. Automatica,1981,17 (1): 23-39.
[175]Unbehauen H, Rao G P. Continuous-time approaches to system identification:a survey [J]. Automatica,1990,26 (1):23-35.
[176]Unbehauen H, Rao G P. A review of identification in continuous-time system [J]. Annual Reviews in Control,1998,22(1):145-171.
[177]Soderstrom T, Mossberg M. Performance evaluation of methods for identifying continuous-time autoregressive processes [J]. Automatica,2000,36 (1):53-59.
[178]Gillberg J, Ljung L. Frequency-domain identification of continuous-time ARMA models from sampled data [J]. Automatica,2009,45 (6):1371-1378.
[179]Thil S, Gamier H, Gilson M. Third-order cumulants based methods for continuous-time errors-in-variables model identification [J]. Automatica,2008,44 (3):647-658.
[180]Larsson E K, Mossberg M, Soderstrom T. Identification of continuous-time ARX models from irregularly sampled data [J]. IEEE Transactions on Automatic Control,2008,52 (3):417-427.
[181]Mahata K, Fu M. Modeling continuous-time processes via input-to-state filters [J]. Automatica,2006, 42.(7):1073-1084.
[182]Mahata K, Gamier H. Identification of continuous-time errors-in-variables models [J]. Automatica, 2006,42 (9):1477-1490.
[183]Moussaoui S, Brie D, Richard A. Regularization aspects in continuous-time model identification [J]. Automatica,2005,41 (2):197-208.
[184]Ren X M, Rad A B, Chan P T, Lo W L. Online identification of continuous-time with unknown time delay [J]. IEEE Transaction on Automatic Control,2005,50 (9):1418-1422.
[185]Fogel E. System identification via membership set constraints with energy constrained noise [J]. IEEE Transactions on Automatic Control,1979,24(5):752-758.
[186]Fogel E, Huang Y F. On the value of information in system identification bounded noise case [J]. IEEE Transactions on Automatic Control,1982,18(2):229-238.
[187]Bravo J M, Alamo T, Camacho E F. Bounded error identification of systems with time-varying parameters [J]. IEEE Transactions on Automatic Control,2006,51(7):1144-1150.
[188]韩志刚.多层递阶方法理论与应用的进展[J].控制与决策,2001,16(2)：129-132.
[189]Haest M, Bastin G, Gevers M Wertz V. ESPION:an expert system for system identification [J]. Automatica, 1990,26 (1):85-95.
[190]邵青,冯汝鹏.非线性系统模糊辨识的新方法[J].控制与决策,2001,16(1)：83-85.
[191]刘福才,关新平,裴润.基于一种新模糊模型的非线性系统模糊辨识[J].控制理论与应用,2003,20(1)：113-116.
[192]Takagi T, Sugeno M. Fuzzy identification of systems and its application to modeling and control [J]. IEEE Transaction on Systems, Man and Cybernetics,1985,15(1):116-132.
[193]朱耀春.基于基因表达式编程技术的非线性系统辨识研究[D].南京：华北电力大学,2008.
[194]Holland J H. Adaptation in Natural and Artificial Systems [M]. Chicago:The University of Michigan Press,1975.
[195]McCulloch W S, Pitts W. A logic calculus of the ideas imminent in neurons activity [J]. Bulletin of Mathematic Biology,1943,10(5):115-133.
[196]Hebb DO. The organization of behavior [M]. Wiley, New York,1949.
[197]焦李成.神经网络计算[M].西安：西安电子科技大学出版社,1993.
[198]Cechin A L, Pechmann D R, De Oliveira L P L. Optimizing Markovian modeling of chaotic systems with recurrent neural networks [J]. Chaos, Solitons & Fractals,2008,37(5):1317-1327.
[199]Guerra F A, Coelho L D S. Multi-step ahead nonlinear identification of Lorenz's chaotic system using radial basis neural network with learning by clustering and particle swarm optimization [J]. Chaos, Solitons & Fractals,2008,37(5):967-779.
[200]丛爽,高雪鹏.几种递归神经网络及其在系统辨识中的应用[J].系统工程与电子技术,2003,25(2)：194-197.
[201]Zhang Q H, Benreniste A. Wavelet networks [J]. IEEE Transactions on Neural Network,1992,3(6): 889-898.
[202]邓韧,李著信,樊友洪.一类递归小波神经网络的稳定性研究[J].应用数学和力学,2007,28(4)：428-432.
[203]Kreinovich V, Sirisaengtaksin O, Cabrera S. Wavelet neural networks are asymptotically optimal approximators for functions of one variable [C]. IEEE International Conference on Neural Networks, 2002:2174-2179.
[204]李臣明,韩子鹏,孔建国.基于自适应小波正交基神经网络的参数辨识[J].火力与指挥控制,2006,31(6)：56-59.
[205]刘则毅,喻文焕.用小波网络辨识离散非线性系统[J].系统科学与数学,2005,25(4)：187-195.
[206]Zadeh L A. From circuit theory to system theory [J]. Proc. IRE,1962,50(5):856-865.
[207]Eykhoff P. System identification—parameter and state estimation [M]. John Wiley& Sons., INC, 1974.
[208]Ljung L. Convergence analysis of parametric identification methods [J]. IEEE Transactions on Automatic Control,1978, AC-23:770-783.
[209]Qin S J, Lin W, Ljung L. A novel subspace identification approach with enforced causal models [J]. Automatica,2005,41(2):2043-2053.
[210]Wang J, Qin S J. Closed-loop subspace identification using the parity space [J]. Automatica,2006, 42(2):315-320.
[211]Favoreel W, De Moor B, Van Overschee P. Subspace identification of bilinear systems subject to white inputs [J]. IEEE Transactions onAutomatic Control,1999,44(9):1157-1165.
[212]Van Overschee P, De Moor B. A unifying theorem for three subspace system identification algorithms [J]. Automatica,1995,31(12):1853-1864.
[213]Wang J, Qin S J. A new subspace identification approach based on principal component analysis [J]. Journal of Process Control,2002,23(12):841-855.
[214]吴祁宗.运筹学与最优化方法[M].北京：机械工业出版社,2003.
[215]席少林.最优化计算方法[M].北京：社会出版社,1983.
[216]Kennedy J, Eberhart R C. Particle swarm optimization [C]. In Proceedings of IEEE International Conference on Neural Networks, Perth, WA, Australia,1995:1942-1948.
[217]Eberhart R C, Kennedy J. A new optimizer using particle swarm theory [C]. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan,1995:39-43.
[218]Kennedy J, Eberhart R C, Shi Y. Swarm intelligence [M]. San Francisco:Morgan Kaufmann Publishers,2001.
[219]Kennedy J, Eberhart R C.A discrete binary version of the particle swarm algorithm [C]. In Proceedings 1997 Conference on Systems, Man, and Cybernetics, Piscataway, NJ:IEEE Service Center,1997:4104-4108.
[220]杨维,李歧强.粒子群优化算法综述[J].中国工程科学,2004,6(5)：87-94.
[221]朱丽莉,杨志鹏,袁华.粒子群优化算法分析及研究进展[J].计算机工程与应用,2007,43(5)：24-27.
[222]Eberhart R C, Shi Y. Particle swarm optimization:developments, application and resources [C]. In Proceedings 2001 Congress on Evolutionary Computation, Seoul, South Korea,2001:81-86.
[223]Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space [J]. IEEE Transaction on Evolutionary Computation,2002,6(1):58-73.
[224]Van Den Bergh F. An analysis of particle swarm optimizers [D]. PhD Dissertation, South Africa: Department of Computer Science, University of Pretoria,2002.
[225]Kennedy J. The particle swarm:social adaptation of knowledge [C]. In Proceedings of IEEE International Conference on Evolutionary Computation, Indianapolis, IN,1997:303-308.
[226]Parsopoulos K E, Vrahatis M N. Recent approaches to global optimization problems through particle swarm optimization [J]. Natural Computing,2002,1(2-3):235-306.
[227]Scholkopf B, Smola A, Williamson R C, Bartlett P L. New support vector algorithms [J]. Neural Computation,2000,20(7)-.1207-1245.
[228]Vapnik V N. The nature of statistical learning theory [M].2nd Edition, New York:Springer Verlag, 1999.
[229]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42.
[230]邓乃扬,田英杰著.数据挖掘中的新方法——支持向量机[M].北京：电子工业出版社,2004.
[231]Smola A, Scholkopf B, Ratsch G. Linear programs for automatic accuracy control in regression [C]. In 9th International Conference on Artificial Neural Networks, London:IEE, Conference Publications No.470,1999:257-268.
[232]Leonov V P, Shiryaev AN. On a method of calculation of semi-invariants [J]. Theory of Probability and Its Applications,1959,4(3):319-329.
[233]Priestley M B. Spectral analysis and time series [M]. USA San Diego:Academic Press,1981.
[234]刘树安,唐非.基于遗传算法的系统辨识方法研究[J].系统工程理论与实践,2007,30(3)：134-139.
[235]付国江,王少梅,刘舒燕,李宁.改进的速度变异粒子群算法[J].计算机工程与应用,2006,42(13)：50-51.
[236]Prakriya M, Hatzinakos D. Blind identification of linear subsystems of LTI-ZMNL-LTI models with cyclostationary inputs [J]. IEEE Transactions on Signal Processing,1997,45(8):2023-2036.
[237]Greblicki W. Nonlinearity estimation in Hammerstein systems based on ordered observations [J]. IEEE Transactions on Signal Processing,1996,44(5):1224-1233.
[238]Boutayeb M, Rafaralahy H, Darouach M. A robust and recursive identification method for Hammerstein model [C]. In Proceedings of IFAC World Congress, San Francisco, CA,1996: 447-452.
[239]Shi Y, Eberhart RCA modified particle swarm optimizer [C]. In Proceeding of the IEEE Congress on Evolutionary Computation. USA, Anchorage, IEEE Service Center,1998:69-73.
[240]吴敏,丁雷,曹卫华,徐辰华.一种克服粒子群早熟的混合优化算法[J].控制与决策,2008,23(5)： 511-514,519.
[241]Ding F, Shi Y, Chen T. Auxiliary model-based least-squares identification methods for Hammerstein output-error systems [J]. Systems and Letters,2007,56(1):373-380.
[242]王冬青.基于辅助模型的递推增广最小二乘辨识算法[J].控制理论与应用,2009,26(1)：51-56.
[243]Billings S A, Fakhouri S Y. Identification of a class of nonlinear systems using correlation analysis [J]. Proceedings of IEE,1978,125(7):691-697.
[244]Crama P, Schoukens J. Initial estimates of Wiener and Hammerstein systems using multisine excitation [J]. IEEE Transactions on Instrumentation and Measurement,2001,50:1791-1795.
[245]Hu X, Chen H F. Strong consistence of recursive identification for Wiener systems [J]. Automatica, 2005,41(6):1905-1916.
[246]Chow T W S, Tan H Z. HOS-based nonparametric and parametric methodologies for machine fault detection [J]. IEEE Transactions on Industrial Electronics,2000,47(5):1051-1059.
[247]Vapnik V. Statistical learning theory [M]. New York:John Wiley& Sons,1998.
[248]Tan H Z, Chow T W S. Blind and total identification of ARMA mode in higher order cumulants domain [J]. IEEE Transactions on Industrial Electronics,1999,46(6):1233-1243.
[249]Voss M S, Feng X. A new methodology for emergent system identification using particle swarm optimization (PSO) and the group method of data handling (GMDH) [C]. In Proceedings of Genetic and Evolutionary Computation Conference, New York, USA,2002:1227-1232.
[250]俞欢军, 许宁,张丽平等.混合粒子群优化算法研究[J].信息与控制,2005,34(4)：500-504.
[251]蔡季冰.系统辨识[M].北京：北京理工大学出版社,1989.
[252]Stoica P. On the convergence of an iterative algorithm used for Hammerstein system identification [J]. IEEE Transactions on Automatic Control,1981,26(2):967-969.
[253]Kalafatis A D, Wang L, Cluett W R. Identification of Wiener-type nonlinear systems in a noisy environment [J]. International Journal of Control,1997,66:923-941.
[254]Liu Y, Bai E W. Iterative identification of Hammerstein systems [J]. Automatica,2007,43 (2): 346-354.
[255]向徽,陈宗海.基于Hammerstein模型描述的非线性系统辨识新方法[J].控制理论与应用,2007,24(1)：143-147.
[256]Falkner A H. Iterative technique in the identification of a non-linear system [J]. International Journal of Control,1998,48(1):385-396.
[257]Chernyshov K. Identification of stochastic N-L-N systems using monotone correlations [C]. In Proceedings of 12th IFAC Symposium on System Identification, Santa Barbara, USA,2000: 1134-1141.
[258]Bai E W, Fu M Y. Blind system identification and channel equalization of IIR systems without statistical information [J]. IEEE Transaction on Signal Processing,1999,47:1910-1921.
[259]Cybenko G. Approximation by superpositions of a sigmoid function [J]. Math Control, Signals and Systems,1989,2(4):201-205.
[260]Benveniste A, Juditsky A, Delyon B, et al. Wavelets in identification [C]. In Proceedings of 10th IFAC Symposium of System Identification, Copenhaegen, Denmark,1994:1103-1115.
[261]冯象初,甘小冰,宋国乡.数值泛函与小波分析[M].西安：西安电子科技大学出版社,2003.
[262]韩江洪,李正荣,魏振春.一种自适应粒子群优化算法及其仿真研究[J].系统仿真学报,2006,18(10)：2969-2971.
[2]方崇智,萧德云.过程辨识[M].北京：清华大学出版社,1988.
[3]朱豫才.著.张湘平,虞水俊,孙志强,胡德文.译.过程控制的多变量系统辨识[M].长沙：国防科技大学出版社,2004.
[4]吴广玉.系统辨识与自适应[M].哈尔滨：哈尔滨工业大学出版社,1987.
[5]刘福才.非线性系统的模糊模型辨识及其应用[M].北京：国防工业出版社,2006.
[6]侯媛彬,汪梅,王立琦.系统辨识及其MATLAB仿真[M].北京：科学出版社,2004.
[7]朱全民.非线性系统辨识[J].控制理论与应用,1994,11(6)：641-652.
[8]Giannakis G B, Serpedin E. A bibliography on nonlinear system identification [J]. Signal Processing, 2001,81(3):533-580.
[9]Billings S A. Identification of nonlinear systems—a survey [J]. IEE Proceedings,1980,6:272-285.
[10]Sjoberg J, Zhang Q H, Ljung L, Benveniste A, Deylon B, Glorennec P Y, Hjalmarsson H, Juditsky A. Nonlinear black-box modeling in system identification:a unified overview [J]. Automatica,1995, 31(12):1691-1724.
[11]Juditsky A, Hjalmarsson H, Benveniste A, Deylon B, Ljung L, Sjoberg J, Zhang Q H. Nonlinear black-box models in system identification:mathematical foundations [J]. Automatica,1995,31(12): 1725-1750.
[12]Vajk I, Hetthessy J. Identification of nonlinear errors-in-variables models [J]. Automatica,2003,39(12): 2099-2107.
[13]Schoukens J, Nemeth J G, Crama P, Rolain Y, Pintelon R. Fast approximate identification of nonlinear systems [J]. Automatica,2003,39(7):1267-1274.
[14]Pia Saccomani M, Audoly S, D'Angio L. Parameter identifiability of nonlinear systems:the role of initial conditions [J]. Automatica,2003,39(4):619-632.
[15]Denis-Vidal L, Joly-Blanchard G. Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems [J]. Automatica,2004,40(2):287-292.
[16]Roll J, Nazin A, Ljung L. Nonlinear system identification via direct weight optimization [J]. Automatica,2005,41(3):475-490.
[17]M kil P M. LTI modelling of NFIR systems:near-linearity and control, LS estimation and linearization [J]. Automatica,2005,41(1):29-41.
[18]M kil P M. On robustness in control and LTI identification:Near-linearity and non-conic uncertainty [J]. Automatica,2006,42(4):601-612.
[19]Wigren T. Recursive prediction error identification and scaling of non-linear state space model using a restricted black box parameterization [J]. Automatica,2006,42(1):159-168.
[20]Anderson S R, Kadirkamanathan V. Modelling and identification of non-linear deterministic systems in the delta-domain [J]. Automatica,2007,43(11):1859-1868.
[21]Bravo J M, Alamo T, Redondo M J, Camacho E F. An algorithm for bounded-error identification of nonlinear systems based on DC functions [J]. Automatica,2008,44(2):437-444.
[22]Yang Z Y, Chan C W. Simultaneous estimation of the input and output frequencies of nonlinear systems [J]. Automatica,2008,44(7):1822-1830.
[23]Xia X, Moog C H. Identifiability of nonlinear systems with application to HIV/AIDS models [J]. IEEE Transactions on Automatic Control,2003,48(2):330-336.
[24]Cao C Y, Annaswamy A M, Kojic A. Parameter convergence in nonlinearly parameterized systems [J]. IEEE Transactions on Automatic Control,2003,48(3):397-412.
[25]Barker H A, Tan A H, Godfrey K R. Optimal levels of perturbation signals for nonlinear systems identification [J]. IEEE Transactions on Automatic Control,2004,49(8):1404-1407.
[26]Li K, Peng J X, Irwin G W. A fast nonlinear model identification method [J]. IEEE Transactions on Automatic Control,2005,50(8):1211-1216.
[27]Espinoza M, Suykens J A K, De Moor B. Kernel based partially linear models and nonlinear identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1602-1606.
[28]Bemporad A, Garulli A, Paoletti S, Vicino A. A bounded-error approach to piecewise affine system identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1567-1580.
[29]Shaw S R, Laughman C R. A method for nonlinear least squares with structured residuals [J]. IEEE Transactions on Automatic Control,2006,51(10):1704-1708.
[30]Zhang J, Xia X, Moog C H. Parameter identifiability of nonlinear systems with time-delay [J]. IEEE Transactions on Automatic Control,2006,51(2):371-375.
[31]Tyukin I Y, Prokhorov D V, Van Leeuwen C. Adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parameterization [J]. IEEE Transactions on Automatic Control, 2007,52(9):1543-1559.
[32]Dalai M, Weyer E, Campi M C. Parameter identification for nonlinear systems:guaranteed confidence regions through LSCR [J]. Automatica,2007,43(8):1418-1425.
[33]Bai E W, Liu Y. Recursive direct weight optimization in nonlinear system identification:a minimal probability approach [J]. IEEE Transactions on Automatic Control,2007,52(7):1218-1231.
[34]Li K, Peng J X, Bai E W. A two-stage algorithm for identification of nonlinear dynamic systems [J]. Automatica,2006,42(7):1189-1197.
[35]Bai E W. Identification of nonlinear additive FIR systems [J]. Automatica,2005,41(7):1247-1253.
[36]李言俊,张科.系统辨识理论及应用[M].北京：国防工业出版社,2003.
[37]衷路生.线性系统的迭代优化与子空间辨识方法研究[D].杭州：浙江大学,2007.
[38]Gevers M. A personal view of the development of system identification:a 30-year journey through an
exciting field [J]. IEEE Control Systems Magazine,2006,26(6):93-105.
[39]Astrom K J, Bohlin T. Numerical identification of linear dynamic systems from normal operating records [C]. In Proceedings of IFAC Symposium on Self-Adaptive Systems, England, Teddington, 1965.
[40]Box G E P, Jenkins G M. Time series analysis, forecasting and control [M]. Oakland, CA:Holden-Day, 1970.
[41]Ljung L. Asymptotic variance expressions for identified black-box transfer function models [J]. IEEE Transactions on Automatic Control,1985, AC-30:834-844.
[42]Ljung L. Development of system identification [C]. In Proceedings of 13th World Congress of IFAC, San Francisco, California,1996, G:141-146.
[43]冯培悌.系统辨识[M].杭州：浙江大学出版社,1999.
[44]柯晶.强跟踪状态估计与群集辨识[D].杭州：浙江大学,2003.
[45]窦立谦,宗群,刘文静.面向控制的系统辨识研究进展[J].系统工程与电子技术,2009,31(1)：158-164.
[46]吴旭光.不确定性系统的鲁棒辨识及其发展[J].控制与决策,1996,11(增刊1)：113-118.
[47]冯旭,孙优贤.鲁棒辨识问题评述[J].控制理论与应用,1993,10(6)：609-616.
[48]莫建林,张卫东,许晓鸣.鲁棒辨识研究的现状[J].控制与决策,2002,17(3)：257-263.
[49]Ljung L, Glover K. Frequency domain versus time domain methods in system identification [J]. Automatica,1981,17(1):71-86.
[50]Mckelvey T, Akcay H, Ljung L. Subspace based on multivariable system identification from frequency response data [J]. IEEE Transactions on Automatic Control,1996,41(7):960-979.
[51]Pintelon R. Frequency domain subspace system identification using non-parametric noise models [J]. Automatica,2002,38(3):1295-1311.
[52]Yang Z J, Sanada S. Frequency domain subspace identification with the aid of the w-operator [J]. Electrical Engineering in Japan,2000,132(1):46-56.
[53]Wills A, Ninnes B, Gibson S. Maximum likelihood estimation of state space models from frequency domain data [J]. IEEE Transactions on Automatic Control,2009,54(1):19-33.
[54]Gillberg J, ljung L. Frequency-domain identification of continues-time ARMA models from sampled data [J]. Automatica,2009,45(6):1371-1378.
[55]Sabri K, El Badaoui M, Guillet F, Adib A, Aboutajdine D. A frequency domain-based approach for blind MIMO system identification using second-order cyclic statistics [J]. Signal Processing,2009, 89(1):77-86.
[56]Trnka P, Havlena V. Subspace like identification incorporating prior information [J]. Automatica,2009, 45(4):1086-1091.
[57]Felici F, Van Wingerden J W, Verhaegen M. Subspace identification of MIMO LPV systems using a
periodic scheduling sequence [J]. Automatica,2007,43(10):1684-1697.
[58]Van Wingerden J W, Verhaegen M. Subspace identification of bilinear and LPV systems for open-and closed-loop data [J]. Automatica,2009,45(2):372-381.
[59]Forssell U, Ljung L. Closed-loop identification revisited [J]. Automatica,1999,35(4):1295-1311.
[60]Miskovic L, Karimi A, Bonvin D, Gevers M. Closed-loop identification of multivariable systems:with or without excitation of all references [J]. Automatica,2008,44(8):2048-2056.
[61]Vanden HPM, Schrama R J P. Identification and control closed-loop issues [J]:Automatica,1995, 31(12):1751-1770.
[62]Qin S J, Lin W, Ljung L. A novel subspace identification approach with enforced causal models [J]. Automatica,2005,41(12):2043-2053.
[63]Chiuso A, Picci G. Consistency analysis of some closed-loop subspace identification methods [J]. Automatica,2005,41(2):377-391.
[64]Niedzwiecki M. On the lower smoothing bound in identification of time-varying systems [J]. Automatica,2008,44(2):459-464.
[65]Niedzwiecki M. Optimal and suboptimal smoothing algorithms for identification of time-varying systems with randomly drifting parameters [J]. Automatica,2008,44(7):1718-1727.
[66]Niedzwiecki M. On "cheap smoothing" opportunities in identification of time-varying systems [J]. Automatica,2008,44(5):1191-1200.
[67]Pillonetto G. Identification of time-varying systems in reproducing kernel Hilbert spaces [J]. IEEE Transactions on Automatic Control,2008,53(9):2202-2209.
[68]Pereira da Silva P S, Batista S. On state representation of time-varying nonlinear systems [J]. Automatica,2009,45(5):1260-1264.
[69]戴汝为,周等勇.智能控制与适应性[C].第三届全球智能控制与自动化大会,安徽,合肥,2001：11-17.
[70]王行愚.系统辨识的若干新动向[J].控制理论与应用,1992,9(3)：319-321.
[71]胡德文.非线性与多变量系统相关辨识[M].长沙：国防科技大学出版社,2001.
[72]Volterra V. Theory of functions [M]. Elackie, London,1930.
[73]Suleiman W, Monin A. New method for identifying finite degree Volterra series [J]. Automatica,2008, 44(2):488-497.
[74]金哲,宋执环,何加铭.基于简化Volterra级数的射频功率放大器建模与辨识[J].电路与系统学报,2008,13(5)：90-94.
[75]王文正,何开锋,欧文,韩崇昭.基于Volterra泛函级数的非线性系统的鲁棒辨识[J].控制理论与应用,2003,20(3)：432-436.
[76]欧文,韩崇昭,王文正.Volterra泛函级数在非线性系统辨识中的应用[J].控制与决策,2002,17(2)：239-242.
[77]魏瑞轩,韩崇昭.一种基于Volterra模型的非线性系统具有全解耦结构的递阶式自适应辨识方法[J].控制理论与应用,2002,19(2)：313-316.
[78]习毅,潘丰.基于Hammerstein模型的非线性自适应预测函数控制[J].系统工程与电子技术,2008,30(11)：2237-2240.
[79]丁宝苍,李少远.具有约束的Hammerstein非线性控制系统的设计与分析[J].控制与决策,2003,18(1)：24-28.
[80]Haddad W M, Chellaboina V S. Nonlinear control of Hammerstein systems with passive nonlinear dynamics [J]. IEEE Transactions on Automatic Control,2001,46(10):1630-1634.
[81]Yoshitani N, Hasegawa A. Model-based control of strip temperature for the heating furnace in continuous annealing [J]. IEEE Transactions on Control Systems Technology,1998,6(2):146-156.
[82]苏成利,王树青.一种基于Wiener模型的非线性预测控制算法[J].信息与控制,2007,36(1)：86-92.
[83]邓自立,李春波.自校正解耦信息融合Wiener状态预报器[J].系统工程与电子技术,2007,29(5)：805-809.
[84]田彦涛,徐明,陆佑方,陈关荣.基于Wiener模型的混沌系统辨识研究[J].控制与决策,2003,18(1)：24-28.
[85]Narendra K S, Gallman P G. An iterative method for the identification of nonlinear systems using a Hammerstein model [J]. IEEE Transactions on Automatic Control,1966, AC-11:546-550.
[86]Voros J. Parameter identification of discontinuous Hammerstein systems [J]. Automatica,1997,33(6): 1141-1146.
[87]Chang F, Luus R. A noniterative method for identification using Hammerstein model [J]. IEEE Transactions on Automatic Control,1971, AC-16:464-468.
[88]Pawlak M. On the series expansion approach to the identification of Hammerstein systems [J]. IEEE Transactions on Automatic Control,1991,36(6):763-767.
[89]Bai E W. Identification of systems with hard input nonlinearities [C]. In Perspectives in Control, Moheimani R, Ed. New York:Springer Verlag,2001.
[90]Bai E W, Fu M Y. A blind approach to Hammerstein model identification [J]. IEEE Transactions on Signal Processing,2002,50(7):1610-1619.
[91]Bai E W. Frequency domain identification of Hammerstein models [J]. IEEE Transactions on Automatic Control,2003,48(4):530-542.
[92]Vaurent L, Pintelon R, Schoukens J. Blind maximum likelihood identification of Hammerstein systems [J]. Automatica,2008,44(12):3139-3146.
[93]Goethals M I, Pelckmans K, Suykens J A K, De Moor B. Subspace identification of Hammerstein systems using least squares support vector machines [J]. IEEE Transactions on Automatic Control,2005, 50(10):1509-1519.
[94]Greblicki W. Continuous-time Hammerstein system identification from sampled data [J]. IEEE Transactions on Automatic Control,2006,51(7):1195-1200.
[95]黄正良,万百五,韩崇昭.辨识Hammerstein模型的两步法[J].控制理论与应用,1995,12(1)：34-39.
[96]徐桥南,袁振东.Hammerstein系统参数的集员辨识[J].控制理论与应用,1994,11(2)：211-215.
[97]孔金生,万百五.一种多输入单输出Hammerstein系统的集成辨识方法[J].控制理论与应用,2005,22(4)：517-519.
[98]张广莹,邓正隆.基于Adaline的双线性Hammerstein模型在线参数辨识[J].电机与控制学报,2003,7(3)：222-225.
[99]Sznaier M. Computational complexity analysis of set membership identification of Hammerstein and Wiener systems [J]. Automatica,2009,45(3):701-705.
[100]Chen H F. Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block [J]. IEEE Transactions on Automatic Control,2005,50(10): 1612-1617.
[101]Bai E W, Li D. Convergence of the iterative Hammerstein system identification algorithm [J]. IEEE Transactions on Automatic Control,2004,49(11):1929-1940.
[102]Hjalmarsson H, Gunnarsson S, Gevers M. Optimality and suboptimality of iterative identification and control design schemes [C]. In Proceedings of the American Control Conference,1995,4:2559-2563.
[103]Raich R, Zhou G T, Viberg M. Subspace based approaches for Wiener system identification [J]. IEEE Transactions on Automatic Control,2005,50(10):1629-1634.
[104]Greblicki W. Nonparametric identification of Wiener systems [J]. IEEE Transactions on Information Theory,1992,38(10):1487-1493.
[105]Bai E W, Reyland Jr J. Towards identification of Wiener the least amount of a priori information on the nonlinearity [J]. Automatica,2008,44(4):910-919.
[106]Cerone V, Regruto D. Parameter bounds evaluation of Wiener models with noninvertible polynomial nonlinearities [J]. Automatica,2006,42(10):1775-1781.
[107]Sznaier M, Ma W J, Camps O I, Lim H. Risk adjusted set membership identification of Wiener systems [J]. IEEE Transactions on Automatic Control,2009,54(5):1147-1152.
[108]Hagenblad A, Ljung L, Wills A. Maximum likelihood of Wiener models [J]. Automatica,2008,44(11): 2697-2705.
[109]Giri F, Rochdi Y, Chaoui F Z. An analytic geometry approach to Wiener system frequency identification [J]. IEEE Transactions on Automatic Control,2009,54(4):683-696.
[110]黄正良,吴坚,万百五.辨识Wiener模型的一种新方法[J].控制理论与应用,1996,13(3)：326-332.
[111]李世华,吴福保,李奇.一种基于动态人工神经网络的Wiener模型辨识[J].控制理论与应用, 2000,17(1)：92-95.
[112]张广莹,邓正隆.基于小波分析的非线性系统Wiener模型辨识[J].电机与控制学报,2001,5(2)：95-97,128.
[113]许自豪,李嗣福,陈宗海.基于Lag-SBP的Wiener型非线性系统的辨识方法[J].系统仿真学报,2002,14(8)：1053-1055.
[114]黄毅卿,陈翰馥.子系统为ARMA和分段线性函数的Wiener系统的参数辨识[J].应用数学学报,2008,31(6)：961-980.
[115]Boutayeb M, Darouach M. Recursive identification method for MISO Wiener-Hammerstein model [J]. IEEE Transactions on Automatic Control,1995,40(2):287-291.
[116]Bershad N J, Bouchired S, Castanie F. Stochastic analysis of adaptive gradient identification of Wiener-Hammerstein systems for Gaussian inputs [J]. IEEE Transactions on Signal Processing,2000, 48(2):557-560.
[117]柯晶,姜静,乔谊正.应用混合进化策略辨识Wiener-Hammerstain模型[J].系统工程与电子技术,2006,28(7)：1055-1063.
[118]Bai E-W. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems [J]. Automatica,1998,34(3):333-338.
[119]Zhu Y C. Estimation of an N-L-N Hammerstein-Wiener model [J]. Automatica,2002,38(9): 1607-1614.
[120]Crama P, Schoukens J. Hammerstein-Wiener system estimator initialization [J]. Automatica,2004, 40(9):1543-1550.
[121]Park H C, Sung S W, Lee J. Modeling of Hammerstein-Wiener processes with special input test signals [J]. Industrial & Engineering Chemistry Research,2006,45(3):1029-1038.
[122]桂卫华,宋海英,阳春华.Hammerstein-Wiener模型最小二乘向量机辨识及其应用[J].控制理论与应用,2008,25(3)：393-397.
[123]朱燕飞,谭洪舟,章云.一类非线性系统盲辨识算法及其仿真研究[J].系统仿真学报,2008,20(4)：3782-3784.
[124]Bai E W. A blind approach to the Hammerstein-Wiener model identification [J]. Automatica,2002, 38(6):967-979.
[125]Ninness B, Goodwin G C. Estimation of models quality [J]. Automatica,1995,31(1):32-74.
[126]Gevers M. Identification for control [C]. Plenary lecture at the 5th IFAC Symposium on Adaptive Control and Signal Processing, Budapest,1995:1-12.
[127]Gevers M. Identification for control:from the early achievements to the revival of experiment design [J]. European Journal of Control,2005,11(1):1-18.
[128]Milanese M, Taragna M. H∞set membership identification:a survey [J]. Automatica,2005,41(12): 2019-2023.
[129]Hjalmarsson H. From experiment design to closed-loop control [J]. Automatica,2005,41(3):393-438.
[130]Gevers M. Identification for control [J]. Annual Reviews in Control,1998,22(3):95-106.
[131]Gevers M, Ljung L. Optimal experiment designs with respect to the extended model application [J]. Automatica,1986,22(2):543-554.
[132]Hjalmarsson H, Gevers M, De Bruyn F, Leblond J. Identification for control:closing the loop gives more accurate controllers [C]. In Proceedings of IEEE Conference Decision and Control, Orlando, Florida,1994:4150-4155.
[133]Gevers M. Connecting identification and robust control:a new challenge [C]. In 9th IFAC/IFORS Symposium on identification and system parameter estimation, Hungary,1991:123-134.
[134]柴天佑.鲁棒辨识方法研究[J].控制理论与应用,1999,16(1)：47-51.
[135]Chen J, Gu G, Nett C N. Worst case identification of continuous time systems via interpolation [J]. Automatica,1994,30(12):1825-1837.
[136]李异平.l1鲁棒辨识：最小二乘算法及试验设计[J].控制理论与应用,2003,20(4)：492-502.
[137]Chen J. Frequency domain tests for validation of linear fractional uncertain models [J]. IEEE Transactions on Automatic Control,1997,42(6):748-760.
[138]Parrilo P A, Sznaier M. Mixed time/frequency-domain based robust identification [J]. Automatica, 1998,34(11):1375-1389.
[139]Bitmead R, Zang Z. An iterative identification and control strategy [C]. In Proceedings of European Control Conference, Grenoble,1991:1395-1400.
[140]Callafon D, Van Den Hof P. Suboptimal feedback control by a scheme of iterative identification and control design [J]. Mathematical Modelling of Systems,1997,3(10):77-101.
[141]Anderson B D O, Bombois X, Gevers M. Caution in iterative modeling and control design [C]. In Proceedings of the IFAC Conference on Adaptive Systems in Control and Signal Processing, Glasgow, U.K.,1998:13-19.
[142]Holmberg U, Valentinotti S, Bonvin D. An identification for control procedure with robust performance [J]. Control Engineering Practice,2000,8(10):1107-1117.
[143]Akcay H, Heuberger P. A frequency-domain iterative identification algorithm using general orthonormal basis functions [J]. Automatica,2001,37(5):663-674.
[144]Date P, Lanzon A. A combined iterative scheme for identification and control redesigns [J]. International Journal of Adaptive Control and Signal Processing,2004,18(8):629-644.
[145]Hildebrand R, Lecchini A, Solari G, et al. Prefiltering in iterative feedback tuning:optimization of the prefilter for accuracy [J]. IEEE Transactions on Automatic Control,2004,49(10):1801-1805.
[146]Viberg M. Subspace-based methods for the identification of linear time invariant systems [J]. Automatica,1995,31(12):1835-1851.
[147]Favoreel W, De Moor B, Van Overschee P. Subspace state space system identification for industrial processes[J]. Process Control,2000,10(2-3):149-155.
[148]Astrom K J, Eykhoff P. System identification-a survey [J]. Automatica,1971,7(1):123-167.
[149]Box G E, Jenkins G M. Time series analysis, forecasting and control, holden-day series in time series analysis and digital processing [M]. Holden-Day, Oacland, Revised Edition,1976.
[150]Eykhoff P. System identification [M]. Wiley, London,1974.
[151]Goodwin G C, Payne R L. Dynamic system identification:experiments design and data analysis [M]. N. Y., Academic Press 1977.
[152]夏天昌.系统辨识—最小二乘法[M].北京：国防工业出版社,1984.
[153]Kung S Y. A new identification method and reduction algorithm via singular value decomposion [C]. In 12th Asilomar Conference on Circuits and Systems, CA,1978.
[154]Lew J S, Juang N, Longman R W. Comparision of several system identification methods for flexible structures [J]. Journal of Vibration,1993,167(2):461-480.
[155]Moonen M, De Moor B,et al. On-line and off-line identification of linear state space models [J]. International Journal of Control,1989,49(1):219-232.
[156]Arun K S, Kung S Y. Balanced approximation of stochastic system [J]. SIAM Journal of Matrix Analysis and Application,1990,11(1):42-68.
[157]Westwick D, Verhaegen M. Identifying MIMO Wiener systems using subspace model identification methods [J]. Signal Processing,1996,52(2):235-258.
[158]Verhaegen M, Westwick D. Identifying MIMO Hammerstein systems in the context of subspace model identification methods [J]. International Journal of Control,1996,63(2):331-349.
[159]Verhaegen M, Yu X D. A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems [J]. Automatica,1995,31(2):201-216.
[160]Verdult V, Verhaegen M. Subspace identification of multivariable linear parameter-varying systems [J]. Automatica,2002,38(5):805-814.
[161]Van Overschee P, De Moor B. Continuous-time frequency domain subspace system identification [J]. Signal Processing,1996,52(2):179-194.
[162]Ohsumi A, Kameyama K, Yamaguchi K I. Subspace identification for continuous-time stochastic systems via distribution-based approach [J]. Automatica,2002,38(1):63-79.
[163]Ljung L, Gunnarsson S. Adaptation and tracking in system identification [J]. Automatica,1990,26(1): 7-21.
[164]Maciej N. Identification of time-varying processes [M]. New York:Wiley,2000.
[165]何振亚.自适应信号处理[M].北京：科学出版社,2002.
[166]Sun Z X, Zhang Z, Tsao T C. Trajectory tracking and disturbance rejection for linear time-varying system:input/output representation [J]. Systems & Control Letters,2009,58 (6):452-460.
[167]Joensen A, Madsen H, Nielsen H A, Nielsen T S. Tracking time-varying parameters with local regression [J]. Automatica,2000,36 (8):1199-1204.
[168]Zhou Q G, Cluett W R. Recursive identification of time-varying systems via incremental estimation [J]. Automatica,1996,32 (10):1427-1431.
[169]Bai E W, Huang Y F. Variable gain parameter estimation algorithms for fast tracking and smooth steady state [J]. Automatica,2000,36 (7):1001-1008.
[170]Lozano R, Dimogianopoulos D, Mahony R. Identification of linear time-varying systems using a modified least-squares algorithm [J]. Automatica,2000,36 (7):1009-1015.
[171]Xue Y C, Qian J X. A modified recursive least squares algorithm with variable parameters and resetting for time-varying system [J]. Chinese Journal of Chemical Engineering,2002,10 (3):298-303.
[172]Sandberg H. A case study in model reduction of linear time-varying systems [J]. Automatica,2006,42 (7):467-472.
[173]Xu J X, Pan Y J, Lee T H. A VSS identification.scheme for time-varying parameters [J]., Automatica, 2003,39 (4):727-734.
[174]Young P. Parameter estimation for continuous-time models:a survey [J]. Automatica,1981,17 (1): 23-39.
[175]Unbehauen H, Rao G P. Continuous-time approaches to system identification:a survey [J]. Automatica,1990,26 (1):23-35.
[176]Unbehauen H, Rao G P. A review of identification in continuous-time system [J]. Annual Reviews in Control,1998,22(1):145-171.
[177]Soderstrom T, Mossberg M. Performance evaluation of methods for identifying continuous-time autoregressive processes [J]. Automatica,2000,36 (1):53-59.
[178]Gillberg J, Ljung L. Frequency-domain identification of continuous-time ARMA models from sampled data [J]. Automatica,2009,45 (6):1371-1378.
[179]Thil S, Gamier H, Gilson M. Third-order cumulants based methods for continuous-time errors-in-variables model identification [J]. Automatica,2008,44 (3):647-658.
[180]Larsson E K, Mossberg M, Soderstrom T. Identification of continuous-time ARX models from irregularly sampled data [J]. IEEE Transactions on Automatic Control,2008,52 (3):417-427.
[181]Mahata K, Fu M. Modeling continuous-time processes via input-to-state filters [J]. Automatica,2006, 42.(7):1073-1084.
[182]Mahata K, Gamier H. Identification of continuous-time errors-in-variables models [J]. Automatica, 2006,42 (9):1477-1490.
[183]Moussaoui S, Brie D, Richard A. Regularization aspects in continuous-time model identification [J]. Automatica,2005,41 (2):197-208.
[184]Ren X M, Rad A B, Chan P T, Lo W L. Online identification of continuous-time with unknown time delay [J]. IEEE Transaction on Automatic Control,2005,50 (9):1418-1422.
[185]Fogel E. System identification via membership set constraints with energy constrained noise [J]. IEEE Transactions on Automatic Control,1979,24(5):752-758.
[186]Fogel E, Huang Y F. On the value of information in system identification bounded noise case [J]. IEEE Transactions on Automatic Control,1982,18(2):229-238.
[187]Bravo J M, Alamo T, Camacho E F. Bounded error identification of systems with time-varying parameters [J]. IEEE Transactions on Automatic Control,2006,51(7):1144-1150.
[188]韩志刚.多层递阶方法理论与应用的进展[J].控制与决策,2001,16(2)：129-132.
[189]Haest M, Bastin G, Gevers M Wertz V. ESPION:an expert system for system identification [J]. Automatica, 1990,26 (1):85-95.
[190]邵青,冯汝鹏.非线性系统模糊辨识的新方法[J].控制与决策,2001,16(1)：83-85.
[191]刘福才,关新平,裴润.基于一种新模糊模型的非线性系统模糊辨识[J].控制理论与应用,2003,20(1)：113-116.
[192]Takagi T, Sugeno M. Fuzzy identification of systems and its application to modeling and control [J]. IEEE Transaction on Systems, Man and Cybernetics,1985,15(1):116-132.
[193]朱耀春.基于基因表达式编程技术的非线性系统辨识研究[D].南京：华北电力大学,2008.
[194]Holland J H. Adaptation in Natural and Artificial Systems [M]. Chicago:The University of Michigan Press,1975.
[195]McCulloch W S, Pitts W. A logic calculus of the ideas imminent in neurons activity [J]. Bulletin of Mathematic Biology,1943,10(5):115-133.
[196]Hebb DO. The organization of behavior [M]. Wiley, New York,1949.
[197]焦李成.神经网络计算[M].西安：西安电子科技大学出版社,1993.
[198]Cechin A L, Pechmann D R, De Oliveira L P L. Optimizing Markovian modeling of chaotic systems with recurrent neural networks [J]. Chaos, Solitons & Fractals,2008,37(5):1317-1327.
[199]Guerra F A, Coelho L D S. Multi-step ahead nonlinear identification of Lorenz's chaotic system using radial basis neural network with learning by clustering and particle swarm optimization [J]. Chaos, Solitons & Fractals,2008,37(5):967-779.
[200]丛爽,高雪鹏.几种递归神经网络及其在系统辨识中的应用[J].系统工程与电子技术,2003,25(2)：194-197.
[201]Zhang Q H, Benreniste A. Wavelet networks [J]. IEEE Transactions on Neural Network,1992,3(6): 889-898.
[202]邓韧,李著信,樊友洪.一类递归小波神经网络的稳定性研究[J].应用数学和力学,2007,28(4)：428-432.
[203]Kreinovich V, Sirisaengtaksin O, Cabrera S. Wavelet neural networks are asymptotically optimal approximators for functions of one variable [C]. IEEE International Conference on Neural Networks, 2002:2174-2179.
[204]李臣明,韩子鹏,孔建国.基于自适应小波正交基神经网络的参数辨识[J].火力与指挥控制,2006,31(6)：56-59.
[205]刘则毅,喻文焕.用小波网络辨识离散非线性系统[J].系统科学与数学,2005,25(4)：187-195.
[206]Zadeh L A. From circuit theory to system theory [J]. Proc. IRE,1962,50(5):856-865.
[207]Eykhoff P. System identification—parameter and state estimation [M]. John Wiley& Sons., INC, 1974.
[208]Ljung L. Convergence analysis of parametric identification methods [J]. IEEE Transactions on Automatic Control,1978, AC-23:770-783.
[209]Qin S J, Lin W, Ljung L. A novel subspace identification approach with enforced causal models [J]. Automatica,2005,41(2):2043-2053.
[210]Wang J, Qin S J. Closed-loop subspace identification using the parity space [J]. Automatica,2006, 42(2):315-320.
[211]Favoreel W, De Moor B, Van Overschee P. Subspace identification of bilinear systems subject to white inputs [J]. IEEE Transactions onAutomatic Control,1999,44(9):1157-1165.
[212]Van Overschee P, De Moor B. A unifying theorem for three subspace system identification algorithms [J]. Automatica,1995,31(12):1853-1864.
[213]Wang J, Qin S J. A new subspace identification approach based on principal component analysis [J]. Journal of Process Control,2002,23(12):841-855.
[214]吴祁宗.运筹学与最优化方法[M].北京：机械工业出版社,2003.
[215]席少林.最优化计算方法[M].北京：社会出版社,1983.
[216]Kennedy J, Eberhart R C. Particle swarm optimization [C]. In Proceedings of IEEE International Conference on Neural Networks, Perth, WA, Australia,1995:1942-1948.
[217]Eberhart R C, Kennedy J. A new optimizer using particle swarm theory [C]. In Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan,1995:39-43.
[218]Kennedy J, Eberhart R C, Shi Y. Swarm intelligence [M]. San Francisco:Morgan Kaufmann Publishers,2001.
[219]Kennedy J, Eberhart R C.A discrete binary version of the particle swarm algorithm [C]. In Proceedings 1997 Conference on Systems, Man, and Cybernetics, Piscataway, NJ:IEEE Service Center,1997:4104-4108.
[220]杨维,李歧强.粒子群优化算法综述[J].中国工程科学,2004,6(5)：87-94.
[221]朱丽莉,杨志鹏,袁华.粒子群优化算法分析及研究进展[J].计算机工程与应用,2007,43(5)：24-27.
[222]Eberhart R C, Shi Y. Particle swarm optimization:developments, application and resources [C]. In Proceedings 2001 Congress on Evolutionary Computation, Seoul, South Korea,2001:81-86.
[223]Clerc M, Kennedy J. The particle swarm-explosion, stability and convergence in a multidimensional complex space [J]. IEEE Transaction on Evolutionary Computation,2002,6(1):58-73.
[224]Van Den Bergh F. An analysis of particle swarm optimizers [D]. PhD Dissertation, South Africa: Department of Computer Science, University of Pretoria,2002.
[225]Kennedy J. The particle swarm:social adaptation of knowledge [C]. In Proceedings of IEEE International Conference on Evolutionary Computation, Indianapolis, IN,1997:303-308.
[226]Parsopoulos K E, Vrahatis M N. Recent approaches to global optimization problems through particle swarm optimization [J]. Natural Computing,2002,1(2-3):235-306.
[227]Scholkopf B, Smola A, Williamson R C, Bartlett P L. New support vector algorithms [J]. Neural Computation,2000,20(7)-.1207-1245.
[228]Vapnik V N. The nature of statistical learning theory [M].2nd Edition, New York:Springer Verlag, 1999.
[229]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42.
[230]邓乃扬,田英杰著.数据挖掘中的新方法——支持向量机[M].北京：电子工业出版社,2004.
[231]Smola A, Scholkopf B, Ratsch G. Linear programs for automatic accuracy control in regression [C]. In 9th International Conference on Artificial Neural Networks, London:IEE, Conference Publications No.470,1999:257-268.
[232]Leonov V P, Shiryaev AN. On a method of calculation of semi-invariants [J]. Theory of Probability and Its Applications,1959,4(3):319-329.
[233]Priestley M B. Spectral analysis and time series [M]. USA San Diego:Academic Press,1981.
[234]刘树安,唐非.基于遗传算法的系统辨识方法研究[J].系统工程理论与实践,2007,30(3)：134-139.
[235]付国江,王少梅,刘舒燕,李宁.改进的速度变异粒子群算法[J].计算机工程与应用,2006,42(13)：50-51.
[236]Prakriya M, Hatzinakos D. Blind identification of linear subsystems of LTI-ZMNL-LTI models with cyclostationary inputs [J]. IEEE Transactions on Signal Processing,1997,45(8):2023-2036.
[237]Greblicki W. Nonlinearity estimation in Hammerstein systems based on ordered observations [J]. IEEE Transactions on Signal Processing,1996,44(5):1224-1233.
[238]Boutayeb M, Rafaralahy H, Darouach M. A robust and recursive identification method for Hammerstein model [C]. In Proceedings of IFAC World Congress, San Francisco, CA,1996: 447-452.
[239]Shi Y, Eberhart RCA modified particle swarm optimizer [C]. In Proceeding of the IEEE Congress on Evolutionary Computation. USA, Anchorage, IEEE Service Center,1998:69-73.
[240]吴敏,丁雷,曹卫华,徐辰华.一种克服粒子群早熟的混合优化算法[J].控制与决策,2008,23(5)： 511-514,519.
[241]Ding F, Shi Y, Chen T. Auxiliary model-based least-squares identification methods for Hammerstein output-error systems [J]. Systems and Letters,2007,56(1):373-380.
[242]王冬青.基于辅助模型的递推增广最小二乘辨识算法[J].控制理论与应用,2009,26(1)：51-56.
[243]Billings S A, Fakhouri S Y. Identification of a class of nonlinear systems using correlation analysis [J]. Proceedings of IEE,1978,125(7):691-697.
[244]Crama P, Schoukens J. Initial estimates of Wiener and Hammerstein systems using multisine excitation [J]. IEEE Transactions on Instrumentation and Measurement,2001,50:1791-1795.
[245]Hu X, Chen H F. Strong consistence of recursive identification for Wiener systems [J]. Automatica, 2005,41(6):1905-1916.
[246]Chow T W S, Tan H Z. HOS-based nonparametric and parametric methodologies for machine fault detection [J]. IEEE Transactions on Industrial Electronics,2000,47(5):1051-1059.
[247]Vapnik V. Statistical learning theory [M]. New York:John Wiley& Sons,1998.
[248]Tan H Z, Chow T W S. Blind and total identification of ARMA mode in higher order cumulants domain [J]. IEEE Transactions on Industrial Electronics,1999,46(6):1233-1243.
[249]Voss M S, Feng X. A new methodology for emergent system identification using particle swarm optimization (PSO) and the group method of data handling (GMDH) [C]. In Proceedings of Genetic and Evolutionary Computation Conference, New York, USA,2002:1227-1232.
[250]俞欢军, 许宁,张丽平等.混合粒子群优化算法研究[J].信息与控制,2005,34(4)：500-504.
[251]蔡季冰.系统辨识[M].北京：北京理工大学出版社,1989.
[252]Stoica P. On the convergence of an iterative algorithm used for Hammerstein system identification [J]. IEEE Transactions on Automatic Control,1981,26(2):967-969.
[253]Kalafatis A D, Wang L, Cluett W R. Identification of Wiener-type nonlinear systems in a noisy environment [J]. International Journal of Control,1997,66:923-941.
[254]Liu Y, Bai E W. Iterative identification of Hammerstein systems [J]. Automatica,2007,43 (2): 346-354.
[255]向徽,陈宗海.基于Hammerstein模型描述的非线性系统辨识新方法[J].控制理论与应用,2007,24(1)：143-147.
[256]Falkner A H. Iterative technique in the identification of a non-linear system [J]. International Journal of Control,1998,48(1):385-396.
[257]Chernyshov K. Identification of stochastic N-L-N systems using monotone correlations [C]. In Proceedings of 12th IFAC Symposium on System Identification, Santa Barbara, USA,2000: 1134-1141.
[258]Bai E W, Fu M Y. Blind system identification and channel equalization of IIR systems without statistical information [J]. IEEE Transaction on Signal Processing,1999,47:1910-1921.
[259]Cybenko G. Approximation by superpositions of a sigmoid function [J]. Math Control, Signals and Systems,1989,2(4):201-205.
[260]Benveniste A, Juditsky A, Delyon B, et al. Wavelets in identification [C]. In Proceedings of 10th IFAC Symposium of System Identification, Copenhaegen, Denmark,1994:1103-1115.
[261]冯象初,甘小冰,宋国乡.数值泛函与小波分析[M].西安：西安电子科技大学出版社,2003.
[262]韩江洪,李正荣,魏振春.一种自适应粒子群优化算法及其仿真研究[J].系统仿真学报,2006,18(10)：2969-2971.