Small-Gain Approach for Adaptive Optimal Control of Switched Nonlinear Systems With Unstable Dynamics

Licheng Zheng, Zhi Liu, C. L. Philip Chen, Yun Zhang, Zongze Wu

Abstract: This article addresses the adaptive optimal tracking control problem of nonlinear switched systems with unstable unmodeled dynamics. One challenge is how to find the optimal control strategy for a modeled x-dynamic system containing the unmodeled dynamics. Another challenge is how to achieve both optimality and stability of the closed-loop system with unstable dynamics. To this end, a novel solution combines adaptive dynamic programming and the small-gain approach, integrating integral penalties on control, states, and unstable dynamics via actor–critic learning and nonzero game mechanisms. The small-gain approach links closed-loop optimality and stability. For unstable dynamics, stability analysis employs a combined fast-slow switching strategy with gain allocation satisfying the small-gain theorem conditions; optimality analysis compensates unstable dynamics via adaptive parameter estimation and derives the optimal controller via a two-player game. Under small-gain conditions, the designed optimal controller ensures closed-loop output tracks reference signals with ultimately bounded errors. Finally, simulation results validate the proposed approach.

External IDs:dblp:journals/tsmc/ZhengLCZW26