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Robust Tracking Control for Non-Zero-Sum Games of Continuous-Time Uncertain Nonlinear Systems
| Content Provider | MDPI |
|---|---|
| Author | Qin, Chunbin Shang, Ziyang Zhang, Zhongwei Zhang, Dehua Zhang, Jishi |
| Copyright Year | 2022 |
| Description | 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. |
| Starting Page | 1904 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math10111904 |
| Journal | Mathematics |
| Issue Number | 11 |
| Volume Number | 10 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2022-06-02 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Industrial Engineering Adaptive Dynamic Programming (adp) Non-zero-sum (nzs) Games Robust Trajectory Tracking Hamilton–jacobi–bellman (hjb) Equation Uncertain Nonlinear Systems |
| Content Type | Text |
| Resource Type | Article |
