Non‐Fragile Adaptive Sliding Tracking Control for a Nonlinear Uncertain Robotic System With Unknown Actuator Nonlinearities

Abstract

ABSTRACT This article proposes non‐fragile adaptive sliding tracking control strategies for a class of nonlinear uncertain robotic systems subject to unknown actuator nonlinearities and controller perturbations. Firstly, a mathematical model for robot systems with unknown actuator nonlinearities is established. Secondly, the non‐fragile integral sliding surface (NHISS) function and pseudo‐singular non‐fragile integral sliding surface (PNHISS) function are developed, and the sufficient conditions for the existence of performance are derived based on the equivalent control schemes. Furthermore, based on the proposed sliding surface functions, a non‐fragile fixed‐gain adaptive (NFGA) sliding control, on the basis of linear matrix inequality (LMI), and a non‐fragile parameter‐varying adaptive (NPVA) sliding control, using sum‐of‐squares (SOS), are designed correspondingly, and the closed‐loop system stability is analyzed based on the Lyapunov approach. Finally, simulation and experiment results are included to illustrate the effectiveness, non‐fragility, and strong robustness of the proposed control strategies.