Robust Fuzzy-Based Sliding Mode Control for Uncertain Discrete Nonlinear Systems for Achieving Performance Requirements

Abstract

A novel sliding mode fuzzy controller design method is investigated in this paper for uncertain stochastic nonlinear systems described by the Takagi–Sugeno fuzzy model. Applying integral sliding control scheme, a reaching controller is developed such that the trajectory of the system is approximated to the assigned sliding surface to guarantee robustness. Next, a fuzzy controller is designed by the concept of parallel distributed compensation to achieve multiple performance constraints, including individual state variance constraint and strictly input passivity. Besides, some sufficient conditions are derived into linear matrix inequality problem via combining Lyapunov stability criterion, passivity theory, and covariance theory. Using convex optimization algorithm, the required feasible solutions can be directly obtained by solving the derived conditions. Thus, a sliding mode fuzzy controller can be established such that uncertain nonlinear stochastic system achieves robustness, stability, individual state variance constraint, and strictly input passivity at the same time. At last, a simulation result of controlling nonlinear ship steering system is proposed to demonstrate the usefulness and applicability of this paper.