Finite-Time Prescribed Performance Adaptive Control for a Class of Switched Uncertain Nonlinear Systems

This paper investigates a finite-time prescribed performance adaptive control (FTPPAC) scheme for a class of full-state dependent switched uncertain nonlinear systems in the non-strict feedback form. Firstly, a model transformation is introduced to handle unknown control coefficients and unknown nonlinear functions, after which a state observer is designed to estimate the unknown state of the transformed system. Subsequently, the backstepping method and adaptive control are employed to ensure that the tracking error satisfies the pre-designed performance indices. Compared with the traditional design of prescribed performance control (PPC) for switched systems, a novel switching-dependent prescribed performance bound (SDPPB) is presented, which is specifically tailored to satisfy the requirements and characteristics of different subsystems. This design approach allows for the adjustment of the initial value of SDPPB at the switching instants based on the tracking error and subsystem change. Finally, by applying the average dwell time switching and multiple Lyapunov functions method, sufficient conditions for finite-time stability of the closed-loop system are derived. The effectiveness of the proposed control scheme is demonstrated through two simulations.