Fixed-time prescribed performance control of affine parameter-varying systems with an application in aero engines

Abstract

This paper considers the prescribed performance problem for a class of affine parameter-varying systems. First, a novel performance function with a fixed convergence time is used to limit the system’s tracking error so that the system satisfies the steady-state and transient performance constraints. Notably, the performance function proposed in this paper converges within a fixed time, and its initial value can be automatically adjusted according to the initial tracking error. Subsequently, we transform the multi-performance constraint problem into an equivalent stabilization problem through error transformation. Finally, a method called “feedback negative definitization” is developed to design the controller, and the Lyapunov theorem is used to demonstrate the closed-loop system’s stability. Simulation examples on a numerical affine parameter-varying system and a turbofan engine system are provided to show the effectiveness of the proposed method.