Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

作     者：Lv, Yongfeng Na, Jing Yang, Qinmin Wu, Xing Guo, Yu 

作者机构：Kunming Univ Sci & Technol Fac Mech & Elect Engn Kunming 650500 Peoples R China Zhejiang Univ Dept Control Sci & Engn Hangzhou 310027 Zhejiang Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF CONTROL》 (国际控制杂志)

年 卷 期：2016年第89卷第1期

页      面：99-112页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基　　金：National Natural Science Foundation of China State Key Laboratory of Industrial Control Technology, Zhejiang University, China [ICT1548] Marie Curie Intra-European Fellowships: AECE Project [FP7-PEOPLE-2013-IEF-625531] 

主　　题：adaptive control optimal control approximate dynamic programming system identification nonlinear systems 

摘      要：An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.