广义系统的状态估计与反馈镇定
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摘要
本文在深入研究广义系统理论和网络控制方法,饱和控制方法以及奇异摄动系统理论的基础之上,研究了广义系统状态估计与反馈镇定的相关问题,得到了一些新的概念和方法,主要研究内容如下：
(一)提出了广义连续系统的含参数广义Riccati方程,得到了含参数广义Riccati方程解存在的充分和必要条件并给出了其解关于参数的渐近性质.利用该渐近性质,构造了低增益状态反馈控制律使得具有输入饱和的线性广义系统是半全局渐近稳定的,利用增益调节技巧得到了系统全局渐近镇定反馈控制律.同时,当系统具有外界扰动时,分别给出了系统半全局和全局渐近镇定反馈控制律的设计.
(二)研究具有输入饱和的广义系统的半全局输出调节问题.利用含参数广义Riccati方程解的渐近性,在未进行系统分解的基础上,得到了解决具有输入饱和的广义系统半全局输出调节问题的状态反馈控制律设计.
(三)建立了信道传输容量有限条件下广义离散系统编码-解码-观测器以及编码-解码-控制器设计方法,并给出了系统可检测以及可镇定的充分条件.进一步地,当通讯网络存在数据包丢失的情况下,得到了系统可检测和可镇定的充分条件.
(四)建立了广义离散系统新的界实引理.分析表明,广义离散系统容许且满足给定的H∞性能指标等价于增广的广义系统是容许的.在此基础上,给出了H∞滤波存在的充要条件,并将H∞滤波器设计转化为求解一组严格线性矩阵不等式的可行解问题.
(五)提出了“广义奇异摄动系统”的概念,研究了连续时间和离散时间两种情形下广义奇异摄动系统的鲁棒稳定性问题.所考虑的广义奇异摄动系统同时具有时变的非线性扰动和小摄动参数.利用不动点定理和矩阵不等式技巧,分别得到了系统解存在唯一且全局鲁棒指数稳定的不依赖于摄动参数的充分条件.
(六)利用广义连续系统的界实引理和线性变换技巧,得到了广义奇异摄动系统H∞滤波器设计不依赖于摄动参数的线性矩阵不等式方法.
Based on the recent research on the theory of descriptor system and singularly perturbed system, networked control methods and control methods with input satu-ration, this dissertation investigates state estimation and feedback control problems for descriptor systems. The main results in this dissertation are as follows:
1. For continuous descriptor systems, a class of parametric generalized alge-braic Riccati equations are proposed and the necessary and sufficient conditions for the existence of the solutions are obtained. In addition, the asymptotical property of the solution with respect to the parameter is given. Base on the asymptotical prop-erty, low-gain state feedback control law is proposed such that the liner descriptor system with input saturation is semi-globally asymptotically stable. Furthermore, a scheduling technique is proposed and global asymptotical stabilization feedback control law is obtained. For linear continuous-time descriptor systems subject to in-put saturation and external disturbance, simultaneous stabilization feedback control laws in both semi-global and global sense are obtained.
2. Semi-global output regulation problem for linear descriptor systems with input saturation is investigated. Base on the asymptotical property of the solution of the parametric generalized algebraic Riccati equation, state feedback control law is designed to solve the output regular problem which involves no system transfor-mation.
3. Both coder-decoder-estimator and coder-decoder-controller procedures are constructed for linear discrete-time descriptor systems with a limited digital com-munication channel. The sufficient detectable and stabilizable conditions are pro-posed. In addition, when data package lost exists in the communication channel, the sufficient detectable and stabilizable conditions are also proposed.
4. A new bounded real lemma is proposed for discrete descriptor systems, which indicates that the admissibility of the descriptor system with a prescribed H∞level is equivalent to the admissibility of an augmented discrete singular system. Then the necessary and sufficient condition is proposed for the existence of the H∞filtering and an linear matrix inequality based design approach is presented for the desired filter.
5. The concept of "singularly perturbed descriptor systems" is proposed and the robust stability problems for the system in both continuous-time and discrete-time cases are studied. The singularly perturbed descriptor system under considered is with both time-variant nonlinearity and small perturbed parameter. By applying the fixed-point principle and matrix inequality technique, a sufficient condition is presented via linear matrix inequality under which the solution exists and the system is globally exponentially asymptotically stable simultaneously.
6. By applying bounded real lemma of linear continuous-time descriptor sys-tems and linearizing transformation technique, an linear matrix inequality based filtering design approach is presented for linear singularly perturbed descriptor sys-tems. It should be noted that the obtained results are independent of the small parameter, thus the numerical stiff problem can be avoided.
(一)提出了广义连续系统的含参数广义Riccati方程,得到了含参数广义Riccati方程解存在的充分和必要条件并给出了其解关于参数的渐近性质.利用该渐近性质,构造了低增益状态反馈控制律使得具有输入饱和的线性广义系统是半全局渐近稳定的,利用增益调节技巧得到了系统全局渐近镇定反馈控制律.同时,当系统具有外界扰动时,分别给出了系统半全局和全局渐近镇定反馈控制律的设计.
(二)研究具有输入饱和的广义系统的半全局输出调节问题.利用含参数广义Riccati方程解的渐近性,在未进行系统分解的基础上,得到了解决具有输入饱和的广义系统半全局输出调节问题的状态反馈控制律设计.
(三)建立了信道传输容量有限条件下广义离散系统编码-解码-观测器以及编码-解码-控制器设计方法,并给出了系统可检测以及可镇定的充分条件.进一步地,当通讯网络存在数据包丢失的情况下,得到了系统可检测和可镇定的充分条件.
(四)建立了广义离散系统新的界实引理.分析表明,广义离散系统容许且满足给定的H∞性能指标等价于增广的广义系统是容许的.在此基础上,给出了H∞滤波存在的充要条件,并将H∞滤波器设计转化为求解一组严格线性矩阵不等式的可行解问题.
(五)提出了“广义奇异摄动系统”的概念,研究了连续时间和离散时间两种情形下广义奇异摄动系统的鲁棒稳定性问题.所考虑的广义奇异摄动系统同时具有时变的非线性扰动和小摄动参数.利用不动点定理和矩阵不等式技巧,分别得到了系统解存在唯一且全局鲁棒指数稳定的不依赖于摄动参数的充分条件.
(六)利用广义连续系统的界实引理和线性变换技巧,得到了广义奇异摄动系统H∞滤波器设计不依赖于摄动参数的线性矩阵不等式方法.
Based on the recent research on the theory of descriptor system and singularly perturbed system, networked control methods and control methods with input satu-ration, this dissertation investigates state estimation and feedback control problems for descriptor systems. The main results in this dissertation are as follows:
1. For continuous descriptor systems, a class of parametric generalized alge-braic Riccati equations are proposed and the necessary and sufficient conditions for the existence of the solutions are obtained. In addition, the asymptotical property of the solution with respect to the parameter is given. Base on the asymptotical prop-erty, low-gain state feedback control law is proposed such that the liner descriptor system with input saturation is semi-globally asymptotically stable. Furthermore, a scheduling technique is proposed and global asymptotical stabilization feedback control law is obtained. For linear continuous-time descriptor systems subject to in-put saturation and external disturbance, simultaneous stabilization feedback control laws in both semi-global and global sense are obtained.
2. Semi-global output regulation problem for linear descriptor systems with input saturation is investigated. Base on the asymptotical property of the solution of the parametric generalized algebraic Riccati equation, state feedback control law is designed to solve the output regular problem which involves no system transfor-mation.
3. Both coder-decoder-estimator and coder-decoder-controller procedures are constructed for linear discrete-time descriptor systems with a limited digital com-munication channel. The sufficient detectable and stabilizable conditions are pro-posed. In addition, when data package lost exists in the communication channel, the sufficient detectable and stabilizable conditions are also proposed.
4. A new bounded real lemma is proposed for discrete descriptor systems, which indicates that the admissibility of the descriptor system with a prescribed H∞level is equivalent to the admissibility of an augmented discrete singular system. Then the necessary and sufficient condition is proposed for the existence of the H∞filtering and an linear matrix inequality based design approach is presented for the desired filter.
5. The concept of "singularly perturbed descriptor systems" is proposed and the robust stability problems for the system in both continuous-time and discrete-time cases are studied. The singularly perturbed descriptor system under considered is with both time-variant nonlinearity and small perturbed parameter. By applying the fixed-point principle and matrix inequality technique, a sufficient condition is presented via linear matrix inequality under which the solution exists and the system is globally exponentially asymptotically stable simultaneously.
6. By applying bounded real lemma of linear continuous-time descriptor sys-tems and linearizing transformation technique, an linear matrix inequality based filtering design approach is presented for linear singularly perturbed descriptor sys-tems. It should be noted that the obtained results are independent of the small parameter, thus the numerical stiff problem can be avoided.
引文
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