Adaptive Output Tracking Control of Piecewise Affine Systems With Prescribed Performance
研究了多输入多输出分段仿射系统的自适应输出跟踪控制，通过直接和间接自适应方法确保输出跟踪误差满足预设的稳态和瞬态性能，并建立了任意切换下的稳定性。
In this article, we investigate the adaptive output tracking control for multiinput–multioutput piecewise affine systems with prescribed performance. Both direct and indirect adaptation approaches are studied. Given a desired trajectory, both control approaches ensure the output tracking error to be confined within a performance bound, which prescribes the steady-state tracking error as well as the transient behavior, such as decaying rate and overshoot. We establish novel common Lyapunov functions without solving the conventional Lyapunov equations. Based on these common Lyapunov functions, the stability of the closed-loop system under arbitrary switching is established. Furthermore, the parameter convergence for both direct and indirect approaches is proved under the persistently exciting condition of the input signals. The dynamic gain adjustment technique is incorporated to counter the singularity problem in the indirect adaptation case. Finally, the numerical simulation validates the effectiveness and correctness of the proposed approaches in both direct and indirect adaptation cases.