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. Note to Practitioners—Finite-time stability analysis and quantitative evaluation of control performance are hot topics in the field of control, which play a crucial role in engineering practice. This paper proposes the finite-time prescribed performance adaptive control scheme for a class of switched uncertain nonlinear systems, which can be applied to motion tracking control of servo mechanisms, command tracking of aero-engine and attitude control of spacecraft. It is worth noting that unknown nonlinear dynamics, unknown control coefficients and system state performance constraint problems often exist in practical systems. Therefore, the model transformation is presented to address unknown control coefficients and unknown nonlinear functions. The state observer is used to estimate the unknown state of the transformed system. By designing switching-dependent prescribed performance bound, whose initial value can vary with the subsystem and tracking error, and by utilizing adaptive control method that remains continuous at the switching instant, we ensure that the tracking error satisfies the pre-designed performance indices and that all signals of the closed-loop system are bounded in finite time. In view of the growing demand for transient and steady-state performance in modern industrial production, this control scheme holds promise for practical problem-solving.