Neural-Network-Based Online HJB Solution for Optimal Robust Guaranteed Cost Control of Continuous-Time Uncertain Nonlinear Systems

作     者：Liu, Derong Wang, Ding Wang, Fei-Yue Li, Hongliang Yang, Xiong 

作者机构：Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China 

出 版 物：《IEEE TRANSACTIONS ON CYBERNETICS》 (IEEE Trans. Cybern.)

年 卷 期：2014年第44卷第12期

页      面：2834-2847页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Natural Science Foundation of China [61034002, 61233001, 61273140, 61304086, 61374105, 71232006] Beijing Natural Science Foundation State Key Laboratory of Management and Control for Complex Systems 

主　　题：Adaptive critic designs adaptive/approximate dynamic programming (ADP) Hamilton-Jacobi-Bellman (HJB) equation neural networks optimal robust guaranteed cost control uncertain nonlinear systems 

摘      要：In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton-Jacobi-Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.