基于辅助模型正交匹配追踪的多输入系统迭代辨识算法
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摘要
针对含有未知时滞的多输入输出误差系统的时滞与参数辨识问题,提出一种基于辅助模型的正交匹配追踪迭代算法.首先,由于各输入通道的时滞未知,通过设定输入回归长度,对系统模型进行过参数化,得到一个高维的辨识模型,且辨识模型中参数向量为稀疏向量;然后,基于辅助模型思想和正交匹配追踪算法,在每次迭代过程中,对参数向量和辅助模型的输出进行交互估计,即利用正交匹配追踪算法获得参数向量的估计,再利用参数估计值计算辅助模型的输出,并用辅助模型的输出值代替信息向量中的不可测信息项以更新参数估计;最后,根据参数向量的稀疏特征,获得系统的时滞估计.所提出算法可以利用少量的采样数据信息同时获得系统参数和时滞的估计值.仿真结果表明了所提出算法的有效性.
For the identification of the multiple-input output-error systems with unknown time-delays, an orthogonal matching pursuit iterative algorithm based on the auxiliary model is proposed. Due to the unknown time-delays of each input channel, a highly dimensional identification model with a sparse parameter vector is derived by setting an input regression length and using the overparameterization. Then, based on the auxiliary model idea and the orthogonal matching pursuit(OMP) algorithm, the parameter vector and the output of the auxiliary model are interactively estimated in each iteration, that is, the OMP algorithm is applied to obtain the estimation of the parameter vector, the auxiliary model output is computed by using the estimated parameters, and then the parameter estimation updated by the information vector where the unmeasurable information items are repaced by the auxiliary model outputs. Finally, the time-delays are estimated according to the sparse characteristic of the parameter vector. The proposed method can simultaneously estimate the parameters and time-delays from a few sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithm.
For the identification of the multiple-input output-error systems with unknown time-delays, an orthogonal matching pursuit iterative algorithm based on the auxiliary model is proposed. Due to the unknown time-delays of each input channel, a highly dimensional identification model with a sparse parameter vector is derived by setting an input regression length and using the overparameterization. Then, based on the auxiliary model idea and the orthogonal matching pursuit(OMP) algorithm, the parameter vector and the output of the auxiliary model are interactively estimated in each iteration, that is, the OMP algorithm is applied to obtain the estimation of the parameter vector, the auxiliary model output is computed by using the estimated parameters, and then the parameter estimation updated by the information vector where the unmeasurable information items are repaced by the auxiliary model outputs. Finally, the time-delays are estimated according to the sparse characteristic of the parameter vector. The proposed method can simultaneously estimate the parameters and time-delays from a few sampled data. A simulation example is used to illustrate the effectiveness of the proposed algorithm.
引文
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[14]丁锋.系统辨识新论[M].北京:科学出版社,2013:152-194.(Ding F.Systems identification-New theory and methods[M].Beijing:Science Press,2013:152-194.)
[15]Wang Y J,Ding F.Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model[J].Automatica,2016,71:308-313.
[16]丁锋.系统辨识算法复杂性、收敛性、计算效率研究[J].控制与决策,2016,31(10):1729-1741.(Ding F.Complexity,convergence and computational efficiency for system identification algorithms[J].Control and Decision,2016,31(10):1729-1741.)
[17]Ding F,Liu P X,Liu G.Gradient based and least-squares based iterative identification methods for OE and OEMAsystems[J].Digital Signal Processing,2010,20(3):664-677.
[18]刘艳君,陶太洋,丁锋.多输入动态调节系统的正交匹配追踪迭代辨识算法[J].中南大学学报:自然科学版2017,48(2):389-394.(Liu Y J,Tao T Y,Ding F.Parameter and time-delay estimation for MISO dynamic adjustment systems based on orthogonal matching pursuit iterative algorithm[J].Jof Central South University:Science and Technology2017,48(2):389-394.)
[2]Wang Q G,Guo X,Zhang Y,Direct identification of continuous time delay systems from step responses[J].Jof Process Control,2001,11(5):531-542.
[3]Bedoui S,Ltaief M,Abderrahim K.Hierarchical gradient based identification of discrete-time delay systems[C]Proc of the 52nd IEEE Conf on Decision and Control Florence,2013:4565-4570.
[4]Tropp J A.Just relax:Convex programming methods for identifying sparse signals in noise[J].IEEE Trans on Information Theory,2006,52(3):1030-1051.
[5]Elad M.Sparse and redundant representations:From theory to applications in signal and image processing[M]New York:Springer-Verlag,2010:169-184.
[6]方红,杨海蓉.贪婪算法与压缩感知理论[J].自动化学报,2011,37(12):1413-1421.(Fang H,Yang H R.Greedy algorithms and compressed sensing[J].Acta Automatica Sinica,2011,37(12):1413-1421.)
[7]Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEETrans on Information Theory,2007,53(12):4655-4666.
[8]Blumensath T,Davies M E.Gradient pursuits[J].IEEETrans on Signal Processing,2008,56(6):2370-2382.
[9]Needell D,Tropp J A.CoSaMP:Iterative signal recovery from incomplete and inaccurate samples[J].Applied&Computational Harmonic Analysis,2009,26(3):301-321.
[10]Liu Y J,Tao T Y.A CS recovery algorithm for model and time delay identification of MISO-FIR systems[J]Algorithms,2015,8(3):743-753.
[11]刘艳君,陶太洋,丁锋.MISO系统基于正交匹配追踪算法的参数与时滞联合估计[J].控制与决策,201530(11):2103-2107.(Liu Y J,Tao T Y,Ding F.Parameter and time-delay identification for MISO systems based on orthogonal matching pursuit algorithm[J].Control and Decision2015,30(11):2103-2107.)
[12]陶太洋,刘艳君,丁锋.MISO-FIR系统的梯度追踪辨识算法[J].信息与控制,2016,45(2):151-156.(Tao T Y,Liu Y J,Ding F.Gradient pursuit identification algorithm for MISO-FIR systems[J].Information and Control,2016,45(2):151-156.)
[13]刘艳君,韩雪,丁锋.基于辅助变量的压缩采样匹配追踪闭环系统辨识方法[J].控制与决策,2017,32(10):1837-1843.(Liu Y J,Han X,Ding F.An instrumental variable based compressed sampling matching pursuit method for closed-loop identification[J].Control and Decision,201732(10):1837-1843.)
[14]丁锋.系统辨识新论[M].北京:科学出版社,2013:152-194.(Ding F.Systems identification-New theory and methods[M].Beijing:Science Press,2013:152-194.)
[15]Wang Y J,Ding F.Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model[J].Automatica,2016,71:308-313.
[16]丁锋.系统辨识算法复杂性、收敛性、计算效率研究[J].控制与决策,2016,31(10):1729-1741.(Ding F.Complexity,convergence and computational efficiency for system identification algorithms[J].Control and Decision,2016,31(10):1729-1741.)
[17]Ding F,Liu P X,Liu G.Gradient based and least-squares based iterative identification methods for OE and OEMAsystems[J].Digital Signal Processing,2010,20(3):664-677.
[18]刘艳君,陶太洋,丁锋.多输入动态调节系统的正交匹配追踪迭代辨识算法[J].中南大学学报:自然科学版2017,48(2):389-394.(Liu Y J,Tao T Y,Ding F.Parameter and time-delay estimation for MISO dynamic adjustment systems based on orthogonal matching pursuit iterative algorithm[J].Jof Central South University:Science and Technology2017,48(2):389-394.)