Finite-Time Model-Free Adaptive Control for Discrete-Time Nonlinear Systems

Abstract

This paper addresses the fast trajectory tracking problem for discrete-time nonlinear systems, and whereby a finite-time model-free adaptive control (FMFAC) approach is innovatively devised. Here, the nonlinear systems’ dynamics are completely unknown and the widespread disturbances are considered. The nonparametric dynamic linearization technique and the adaptive extended disturbance observer are firstly deployed to achieve real-time linearization of the discrete-time nonlinear system, and an efficient finite-time performance index function is thereafter devised, and thereby contributing to a novel FMFAC control scheme. Theoretical analysis indicates the finite-time model-free tracking control within a stable region can be guaranteed, and the boundedness of the control input signal can be ensured rigorously, even though under the effect of various disturbances. The key points of the proposed FMFAC approach are model-free and possessing the fast regulation ability, and the corresponding effectiveness and superiority are validated via simulation studies.