Adaptive neural design of fixed-time controllers for MIMO systems with nonlinear static and dynamic interactions

Abstract

Existing fixed-time adaptive neural controllers for uncertain multi-input/multi-output (MIMO) systems with unknown nonlinear interactions only ensure practical fixed-time stabilization or require extra assumptions on system nonlinear functions. To remove these limitations and improve the result to fixed-time stabilization, a dynamic switched Lyapunov function candidate is newly proposed, based on which a novel direct adaptive neural strategy is developed to design fixed-time stable controllers for MIMO systems. To overcome the difficulty in establishing fixed-time stability in the presence of unknown interactions, a two-step Lyapunov function analysis method is proposed to prove that the tracking errors asymptotically converge to preassigned values within a fixed time. Simulation studies substantiate the methods developed.