双态自适应控制问题研究
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摘要
本文主要研究了随机系统中比较典型的一个问题：双态自适应控制。
对于参数已知的随机控制，系统的不确定性是由于其状态与测量受到来自外界的随机干扰而造成的。这种不确定性虽然无法控制或减小，但可以通过一些技术如Kalman滤波等来估计系统的状态以达到最优控制的目的；然而，实际情况往往并非如此，系统在受到外界随机干扰的同时，还会有许多未知的动态行为会引起系统参数发生变化从而造成参数未知。理想的控制器应该在参数未知的情况下仍能够作出合理的决策。目前，常用的方法是常规的自适应控制。常规的自适应控制解决这类问题的基本依据是确定性等价原理，即首先对系统参数进行估计，然后在设计控制器时将参数的估计值当作真值对待。两个阶段独立进行，具有分离性。这种确定性等价原理的严重缺陷在于设计控制器时没有考虑到参数辨识的不精确性。因此，把控制目标与辨识目标结合起来作为一个混合问题考虑，是对确定性等价原理的重大突破，这就是双态控制的本质。随机最优控制策略的双态性质体现在：一方面，控
西安理工大学硕士学位论文
制信号使得系统输山趋向期望的目标（称为对系统的调h作川或控制作川）；另一方
面，控制信号的作川还要有助了减小系统参数的不确定性（称为对参数不确定性的
学习作川成估计作川）。这两种作川在控制律的实现中是矛盾的，前者要求控制信号
的变化趋向平缓，而后者则要求维持一定幅度的激励，状态控制策略就是获取调节
和学习的最佳折衷。
针对厂有恒定的本知参数的随机系统，本文提出了基了两级最优算法的极态向
适应控制；在此基础上，针对未知参数变化的随机系统，本文提出了基丁新息的两
步以态向适应控制。仿真结果表明，这两种壮志向适应控制方法能取得良好的控制
性能和辨识效果；另外，本文对了本知参数在有限个参数集中取值的情况也进行了
研究，针对DUL算法的反应较慢的缺陷，认真分析了控制与辨识这一对矛盾结合体
的关系，提出了一种改进算法，从而人人提高了系统的控制性能。
从态向适应控制问题是日前国际控制界广泛重视的一个随机系统控制问题。本
文对这个问题进行了认真研究，并提出了相应的解决方法，有关定理也给山了证明
过程。
This paper discusses a typical problem of stochastic systems: dual adaptive control.
The uncertainty of a stochastic system with known parameters is the result of the outside unknown disturbances acting on its process and measurement. This class of uncertainty can't be lessened. However, the optimal control can be obtained based on the optimal estimation to the system state by some estimation methods such as Kalman filter. But in practical situations, some unknown dynamic behavior may lead to the change of the system parameters. Therefore it is very common that the systems parameters are unknown. So far the most common solution to this problem is the conventional adaptive control. The technique for designing a conventional adaptive controller is to divide the derivation of the control signal into two parts: state estimation and seeking for the feedback control law with the assumption that the estimated parameters are true. Evidently, the defect of this method is that it doesn't consider the interaction between the identification and the control. So it is a great breakthrough to combine the e
stimation objective and the control objective to a mixed problem, which is the
essence of dual control. An optimal dual controller pursues two often-conflicting objectives: to drive the system toward a desired state, and to perform active learning to reduce the systems uncertainty.
For systems with unknown and invariable parameters, I proposed dual control based on two-level algorithm. Further more, for systems with unknown and variable parameters, I presented innovations two-stage dual control. Simulations show that these two dual control methods can achieve satisfactory control performance and preferable estimation results. In Addition, for systems with parameters limited to several sets, I present an improved DUL algorithm with careful analysis of the relation between control and identification, thus greatly improves the response speed and control performance of the system. .
Dual adaptive control is a control method for stochastic systems that currently causes great attention of the international control society. In this thesis the dual control methods are studied carefully and several new methods are presented and the relevant theorems are also proved in detail.
对于参数已知的随机控制，系统的不确定性是由于其状态与测量受到来自外界的随机干扰而造成的。这种不确定性虽然无法控制或减小，但可以通过一些技术如Kalman滤波等来估计系统的状态以达到最优控制的目的；然而，实际情况往往并非如此，系统在受到外界随机干扰的同时，还会有许多未知的动态行为会引起系统参数发生变化从而造成参数未知。理想的控制器应该在参数未知的情况下仍能够作出合理的决策。目前，常用的方法是常规的自适应控制。常规的自适应控制解决这类问题的基本依据是确定性等价原理，即首先对系统参数进行估计，然后在设计控制器时将参数的估计值当作真值对待。两个阶段独立进行，具有分离性。这种确定性等价原理的严重缺陷在于设计控制器时没有考虑到参数辨识的不精确性。因此，把控制目标与辨识目标结合起来作为一个混合问题考虑，是对确定性等价原理的重大突破，这就是双态控制的本质。随机最优控制策略的双态性质体现在：一方面，控
西安理工大学硕士学位论文
制信号使得系统输山趋向期望的目标（称为对系统的调h作川或控制作川）；另一方
面，控制信号的作川还要有助了减小系统参数的不确定性（称为对参数不确定性的
学习作川成估计作川）。这两种作川在控制律的实现中是矛盾的，前者要求控制信号
的变化趋向平缓，而后者则要求维持一定幅度的激励，状态控制策略就是获取调节
和学习的最佳折衷。
针对厂有恒定的本知参数的随机系统，本文提出了基了两级最优算法的极态向
适应控制；在此基础上，针对未知参数变化的随机系统，本文提出了基丁新息的两
步以态向适应控制。仿真结果表明，这两种壮志向适应控制方法能取得良好的控制
性能和辨识效果；另外，本文对了本知参数在有限个参数集中取值的情况也进行了
研究，针对DUL算法的反应较慢的缺陷，认真分析了控制与辨识这一对矛盾结合体
的关系，提出了一种改进算法，从而人人提高了系统的控制性能。
从态向适应控制问题是日前国际控制界广泛重视的一个随机系统控制问题。本
文对这个问题进行了认真研究，并提出了相应的解决方法，有关定理也给山了证明
过程。
This paper discusses a typical problem of stochastic systems: dual adaptive control.
The uncertainty of a stochastic system with known parameters is the result of the outside unknown disturbances acting on its process and measurement. This class of uncertainty can't be lessened. However, the optimal control can be obtained based on the optimal estimation to the system state by some estimation methods such as Kalman filter. But in practical situations, some unknown dynamic behavior may lead to the change of the system parameters. Therefore it is very common that the systems parameters are unknown. So far the most common solution to this problem is the conventional adaptive control. The technique for designing a conventional adaptive controller is to divide the derivation of the control signal into two parts: state estimation and seeking for the feedback control law with the assumption that the estimated parameters are true. Evidently, the defect of this method is that it doesn't consider the interaction between the identification and the control. So it is a great breakthrough to combine the e
stimation objective and the control objective to a mixed problem, which is the
essence of dual control. An optimal dual controller pursues two often-conflicting objectives: to drive the system toward a desired state, and to perform active learning to reduce the systems uncertainty.
For systems with unknown and invariable parameters, I proposed dual control based on two-level algorithm. Further more, for systems with unknown and variable parameters, I presented innovations two-stage dual control. Simulations show that these two dual control methods can achieve satisfactory control performance and preferable estimation results. In Addition, for systems with parameters limited to several sets, I present an improved DUL algorithm with careful analysis of the relation between control and identification, thus greatly improves the response speed and control performance of the system. .
Dual adaptive control is a control method for stochastic systems that currently causes great attention of the international control society. In this thesis the dual control methods are studied carefully and several new methods are presented and the relevant theorems are also proved in detail.
引文
[1]A. A. Feldbaum.Dual Control Theory Ⅰ-Ⅱ. Automation and Remote Control,vol:21, ⅷ,1960:874-880. 1033-1039.
[2]A.A.Feldbaum.Dual Control Theory Ⅲ-Ⅳ. Automation and Remote Control,vol:22,1961:1-12,109-121.
[3]P.Comon.Independent Component Analysis,A New Concept, Signal Processing,vol:36,1994: 287-314.
[4]符曦编．系统最优化及控制．机械工业出版社．
[5]解学书编．最优控制理论及其应用．清华大学出版社．
[6]梁军．对偶自适应控制．控制理论与应用，1997：297-305．
[7]王伟．多模型自适应控制．科学出版社．
[8]J. Alster,P. R. Belangen. A Technique for Dual Adaptive Control,Automatica,Vol:10,1974: 627-634.
[9]R.Milito,C. S. Padilla, R. A. Padilla and D. Cadorin. An Innovation Approach to Dual Control,IEEE Trans.on Automatic Control,Vol:AC-27,No:1, 1982:132-137.
[10]A. L. Maitelli and T.Yoneyama.Two-stage Suboptimal Dual Controller for Systems With Stochastic Parameters Using Optimal Predictors,IEE. Proc D Control Theory Application,Vol:141, No:4,1994.
[11]A. L. Maitelli and T. Yoneyama.A Multistage Suboptimal Dual Controller Using Optimal Predictors,Automatica, Vol:30,No:12,1999.
[12]H. F. Chen and L. Guo.Convergence Rate of LS Identification and Adaptive Control for Stochastic Systems,Int. J of Control,vol: 44, No: 5,1986:1459-1476.
[13]H. F. Chen and L. Guo. A Robust Stochastic Adaptive Controller,IEEE trans, on Automat Control,vol: 33, No:11,1988:1035-1043.
[14]D. Li, F.C. Qian and P.L Fu.Variance Minimization Approach for a Class of Dual Control Problems,IEEE Trans.on Automatic Control,vol..47, No:12, 2002.
[15]D. Li, F.C. Qian and P.L. Fu.Variance Minimization in Stochastic Systems,In X Y, Zhou(Ed),Stochastic Modeling and Control,Springer,New York,2002.
[16]D. Li, F.C. Qian and P.L. Fu.Variance Minimization Approach for a Class of Dual
Control Problems,American Control Conference,vol:3.2002:3759-3764.
[17]P.L. Fu, D. Li and F.C. Qian. ctive Dual Control for Linear-quadratic Gaussian System with Unknown Parameters,the 15th IFAC Worm Congress, Barcelon,Spain,2002:21-26.
[18]S. Fabri and V.Kadirkamanathan.Dual Adaptive Control of Nonlinear Stochastic Systems using Neural Networks,Automatica,Vol: 34, No:2,1998: 245-253.
[19][美]J.S.麦迪成．随机最优线性估计与控制．黑龙江人民出版社．
[20]B.WittenMark.Stochastic Adaptive Control Methods:a survey,Int.J.Contr,Vol:21,No:5,1975: 705-730.
[21]K.J.(?)str(?)m and B.Wittenmark.Problems of Identification and Control,Journal of Mathematical Analysis and Applications,1971:90-113.
[22]B.Wittenmark. An Active Suboptimal Dual Controller for Systems with Stochastic Parameters,Automatic Control Theory Applications,1975.
[23]J. Sternby.A Simple Dual Control Problem with an Analytical Solution,IEEE Trans.on Automatic contro,AC-21,1976.
[24]G.C.Goodwin,孙贵生．自适应滤波、预测与控制．科学出版社，1992.
[25]S. Amari.Natural Gradient Works efficiently in Learning, Neural Computation,vol:10,1998: 251-276.
[26]E. Tse, B. Shalom and L. Meier.Widen-sense Adaptive Dual Control for Nonlinear Stochastic Systems,IEEE Trans.on Automat. Contr.,AC-18 (2), 1973:98-108.
[27]B. Shalom,Stochastic Dynamic Programming:Cautions and Probing,IEEE Trans.on Automat.Control,vol:26,No:5,1981:1184-1195.
[28]B.Shalom and K.D.Wall.Dual Adaptive Control and Uncertainty Effects in Macroeconomic Systems Optimization,Automatica,Vol:16, No- 2, 1980:147-156.
[29]E. Tse and B. Shalom.Adaptive Dual Control for Stochastic nonlinear systems with Free End-time,IEEE Trans. on Automat.Control, vol:20, No: 5, 1975:670-675.
[30]B. Shalom and E. Tse.Concepts and Mothods in Stochastic Control,Control and Dynamic Systmes,New York,1976:99-172.
[31]E. Tse and B. Shalom. An Actively Adaptive Control for Linear Systems with Random Parameters via the Dnal Control Annroach,IEEE Trans on Automat
Control,vol:18, No: 2,1973: 109-117.
[32]B. Nilsson and A.Wernersson. Active Uncertainty Reduction during Gripping Using Range Cameras-dual Control,Proc.IEEE Conf.on Intelligent Robots and Systems,1995: 406-413.
[33]L. Moreno, et. al..Dynamic Programming Approach for Nonlinear Systems, IEE Proc. D. Control Theory Application,vol:141, No;6,1994: 409-417.
[34]李清泉．自适应控制系统理论、设计与应用．科学出版社，1990．
[35]黄世明．非最小相位系统的最小方差控制．武汉交通科技大学学报．Vol：23，No：2，1999．
[36]J.G. Deshpande,T.N. Upadhyay and D.G. Lainitotis.Adaptive Control of Stochastic Systems, Automatica, vol:9, No: 1,1973:107-115.
[2]A.A.Feldbaum.Dual Control Theory Ⅲ-Ⅳ. Automation and Remote Control,vol:22,1961:1-12,109-121.
[3]P.Comon.Independent Component Analysis,A New Concept, Signal Processing,vol:36,1994: 287-314.
[4]符曦编．系统最优化及控制．机械工业出版社．
[5]解学书编．最优控制理论及其应用．清华大学出版社．
[6]梁军．对偶自适应控制．控制理论与应用，1997：297-305．
[7]王伟．多模型自适应控制．科学出版社．
[8]J. Alster,P. R. Belangen. A Technique for Dual Adaptive Control,Automatica,Vol:10,1974: 627-634.
[9]R.Milito,C. S. Padilla, R. A. Padilla and D. Cadorin. An Innovation Approach to Dual Control,IEEE Trans.on Automatic Control,Vol:AC-27,No:1, 1982:132-137.
[10]A. L. Maitelli and T.Yoneyama.Two-stage Suboptimal Dual Controller for Systems With Stochastic Parameters Using Optimal Predictors,IEE. Proc D Control Theory Application,Vol:141, No:4,1994.
[11]A. L. Maitelli and T. Yoneyama.A Multistage Suboptimal Dual Controller Using Optimal Predictors,Automatica, Vol:30,No:12,1999.
[12]H. F. Chen and L. Guo.Convergence Rate of LS Identification and Adaptive Control for Stochastic Systems,Int. J of Control,vol: 44, No: 5,1986:1459-1476.
[13]H. F. Chen and L. Guo. A Robust Stochastic Adaptive Controller,IEEE trans, on Automat Control,vol: 33, No:11,1988:1035-1043.
[14]D. Li, F.C. Qian and P.L Fu.Variance Minimization Approach for a Class of Dual Control Problems,IEEE Trans.on Automatic Control,vol..47, No:12, 2002.
[15]D. Li, F.C. Qian and P.L. Fu.Variance Minimization in Stochastic Systems,In X Y, Zhou(Ed),Stochastic Modeling and Control,Springer,New York,2002.
[16]D. Li, F.C. Qian and P.L. Fu.Variance Minimization Approach for a Class of Dual
Control Problems,American Control Conference,vol:3.2002:3759-3764.
[17]P.L. Fu, D. Li and F.C. Qian. ctive Dual Control for Linear-quadratic Gaussian System with Unknown Parameters,the 15th IFAC Worm Congress, Barcelon,Spain,2002:21-26.
[18]S. Fabri and V.Kadirkamanathan.Dual Adaptive Control of Nonlinear Stochastic Systems using Neural Networks,Automatica,Vol: 34, No:2,1998: 245-253.
[19][美]J.S.麦迪成．随机最优线性估计与控制．黑龙江人民出版社．
[20]B.WittenMark.Stochastic Adaptive Control Methods:a survey,Int.J.Contr,Vol:21,No:5,1975: 705-730.
[21]K.J.(?)str(?)m and B.Wittenmark.Problems of Identification and Control,Journal of Mathematical Analysis and Applications,1971:90-113.
[22]B.Wittenmark. An Active Suboptimal Dual Controller for Systems with Stochastic Parameters,Automatic Control Theory Applications,1975.
[23]J. Sternby.A Simple Dual Control Problem with an Analytical Solution,IEEE Trans.on Automatic contro,AC-21,1976.
[24]G.C.Goodwin,孙贵生．自适应滤波、预测与控制．科学出版社，1992.
[25]S. Amari.Natural Gradient Works efficiently in Learning, Neural Computation,vol:10,1998: 251-276.
[26]E. Tse, B. Shalom and L. Meier.Widen-sense Adaptive Dual Control for Nonlinear Stochastic Systems,IEEE Trans.on Automat. Contr.,AC-18 (2), 1973:98-108.
[27]B. Shalom,Stochastic Dynamic Programming:Cautions and Probing,IEEE Trans.on Automat.Control,vol:26,No:5,1981:1184-1195.
[28]B.Shalom and K.D.Wall.Dual Adaptive Control and Uncertainty Effects in Macroeconomic Systems Optimization,Automatica,Vol:16, No- 2, 1980:147-156.
[29]E. Tse and B. Shalom.Adaptive Dual Control for Stochastic nonlinear systems with Free End-time,IEEE Trans. on Automat.Control, vol:20, No: 5, 1975:670-675.
[30]B. Shalom and E. Tse.Concepts and Mothods in Stochastic Control,Control and Dynamic Systmes,New York,1976:99-172.
[31]E. Tse and B. Shalom. An Actively Adaptive Control for Linear Systems with Random Parameters via the Dnal Control Annroach,IEEE Trans on Automat
Control,vol:18, No: 2,1973: 109-117.
[32]B. Nilsson and A.Wernersson. Active Uncertainty Reduction during Gripping Using Range Cameras-dual Control,Proc.IEEE Conf.on Intelligent Robots and Systems,1995: 406-413.
[33]L. Moreno, et. al..Dynamic Programming Approach for Nonlinear Systems, IEE Proc. D. Control Theory Application,vol:141, No;6,1994: 409-417.
[34]李清泉．自适应控制系统理论、设计与应用．科学出版社，1990．
[35]黄世明．非最小相位系统的最小方差控制．武汉交通科技大学学报．Vol：23，No：2，1999．
[36]J.G. Deshpande,T.N. Upadhyay and D.G. Lainitotis.Adaptive Control of Stochastic Systems, Automatica, vol:9, No: 1,1973:107-115.