一类未知非线性系统中有限域最优跟踪控制的迭代DHP算法
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摘要
针对一类未知非线性离散时间系统,提出了一种无模型时域有限差分最优跟踪控制方案.在有限时域最优控制理论的框架下,将跟踪控制问题转化为误差动态调节器,引入迭代自适应动态规划(ADP)算法,通过双启发式动态规划(DHP)技术,分别用三个神经网络逼近误差动力学、成本函数和控制率,结合成本函数和控制率的收敛性分析,得到有限时域最优控制器.通过仿真实例验证了跟踪控制方案的有效性.
A model-free finite-horizon optimal tracking control scheme for a class of unknown nonlinear discrete-time systems is proposed in this paper.The tracking control problem is converted into designing a regulator for the tracking error dynamics under the framework of finite-horizon optimal control theory.The iterative adaptive dynamic programming(ADP)algorithm is introduced,via dual heuristic dynamic programming(DHP)technique,three neural networks are taken to approximate the error dynamics,the cost function,and the control law,respectively,with convergence analysis in terms of cost function and control law,obtain the finite-horizon optimal controller.The effectiveness of the tracking control scheme is verified by simulation.
A model-free finite-horizon optimal tracking control scheme for a class of unknown nonlinear discrete-time systems is proposed in this paper.The tracking control problem is converted into designing a regulator for the tracking error dynamics under the framework of finite-horizon optimal control theory.The iterative adaptive dynamic programming(ADP)algorithm is introduced,via dual heuristic dynamic programming(DHP)technique,three neural networks are taken to approximate the error dynamics,the cost function,and the control law,respectively,with convergence analysis in terms of cost function and control law,obtain the finite-horizon optimal controller.The effectiveness of the tracking control scheme is verified by simulation.
引文
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[2]Rushikesh K,Huyen D,Shubhendu B,et al.Approximate optimal trajectory tracking for continuous-time nonlinear systems[J].Automatica,2015,51:40-48.
[3]Kyriakos G V,Arman M,Henrique F.Event-triggered optimal tracking control of nonlinear systems[J].International Journal of Robust and Nonlinear Control,2017,27(4):598-319.
[4]唐功友,刘毅敏,张勇.非线性离散系统的近似最优跟踪控制[J].控制理论与应用,2010,27:1293-1302.
[5]Rushikesh K,Lindsey A,Patrick W,et al.Model-based reinforcement learning for infinite-horizon approximate optimal tracking[J].IEEE Transactions on Neural Networks and Learning Systems,2017,28:753-758.
[6]Jagannathan S.Neural network control of nonlinear discrete-time systems[M].Boca Raton:CRC Press,2006.
[7]张华光,张欣,罗艳红,等.自适应动态规划综述[J].自动化学报,2013,39(4):303-311.
[8]Ruano A E.Intelligent control systems using computational intelligence techniques[M].London:The Institute of Engineering and Technology,2008.
[9]Al-Tamimi A,Lewi F L,Abu-Khalaf M.Discrete-time nonlinear HJB solution using approximate dynamic programming:convergence proof[J].IEEE Transactions on System,Man,Cybernetics,Part B,Cybernetics,2008,38:943-949.
[10]Zhang H,Luo Y,Liu D.Neural-network-based near-optimal control for a class of discrete-time affine nonlinear systems with control constraints[J].IEEE Transactions on Neural Networks,2009,20:1490-1503.
[11]Wang F Y,Jin N,Liu D,et al.Adaptive dynamic programming for finite-horizon optimal control of discrete-time nonlinear systems with error bound[J].IEEE Transactions on Neural Networks,2011,22:24-36.
[12]Wang D,Liu D,Zhang Q,et al.Data-based adaptive critic designs for nonlinear robust optimal control with uncertain dynamics[J].IEEE Transactions on Systems,Man,and Cybernetics:Systems,2016,46:1544-1555.
[13]Dierks T,Jagannathan S.Optimal tracking control of affine nonliner discrete-time systems with unknown internal dynamics[C].Proceedings of Joint 48th IEEE Conference on Decision and Controland 28th Chinese Control Conference,Shanghai,P R China,Dec 2009:6750-6755.
[14]Park Y M,Choi M S,Lee K Y.An optimal tracking neurocontroller for nonlinear dynamic systems[J].IEEE Transactions on Neural Networks,1996(7):1099-1110.