Robust Tracking Control for Non-Zero-Sum Games of Continuous-Time Uncertain Nonlinear Systems

Chunbin Qin, Ziyang Shang, Zhongwei Zhang, Dehua Zhang and Jishi Zhang
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Chunbin Qin: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Ziyang Shang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Zhongwei Zhang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Dehua Zhang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Jishi Zhang: School of Software, Henan University, Kaifeng 475000, China

Mathematics, 2022, vol. 10, issue 11, 1-23

Abstract: In this paper, a new adaptive critic design is proposed to approximate the online Nash equilibrium solution for the robust trajectory tracking control of non-zero-sum (NZS) games for continuous-time uncertain nonlinear systems. First, the augmented system was constructed by combining the tracking error and the reference trajectory. By modifying the cost function, the robust tracking control problem was transformed into an optimal tracking control problem. Based on adaptive dynamic programming (ADP), a single critic neural network (NN) was applied for each player to solve the coupled Hamilton–Jacobi–Bellman (HJB) equations approximately, and the obtained control laws were regarded as the feedback Nash equilibrium. Two additional terms were introduced in the weight update law of each critic NN, which strengthened the weight update process and eliminated the strict requirements for the initial stability control policy. More importantly, in theory, through the Lyapunov theory, the stability of the closed-loop system was guaranteed, and the robust tracking performance was analyzed. Finally, the effectiveness of the proposed scheme was verified by two examples.

Keywords: adaptive dynamic programming (ADP); non-zero-sum (NZS) games; robust trajectory tracking; Hamilton–Jacobi–Bellman (HJB) equation; uncertain nonlinear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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