Fuzzy Lyapunov-Based Model Predictive Sliding-Mode Control of Nonlinear Systems: An Ellipsoid Recursive Feasibility Approach

Abstract

In this article, we introduce the design of an artificial fuzzy Lyapunov-based model predictive integral sliding-mode control to achieve the stability of the closed-loop Takagi–Sugeno fuzzy-model-based nonlinear systems. First, to reach the proper performance against the model uncertainties, a fuzzy integral sliding-mode controller (FISMC) is designed. Then, the fuzzy model predictive control (MPC) is developed based on a fuzzy Lyapunov function by considering a contractive constraint and an ellipsoidal terminal constraint. A systematic method is developed to reach the recursive feasibility of the MPC optimization problem based on an ellipsoidal terminal set. Also, a contractive fuzzy Lyapunov condition is imposed on the fuzzy MPC problem to guarantee the stability of closed-loop systems, which is led to a linear matrix inequality-based generalized eigenvalue minimization problem. In the proposed approach, FISMC greatly improves the robustness property of the fuzzy Lyapunov-based model predictive control and the asymptotic stability of the closed-loop system is achieved in comparison with the tube-based MPC. In addition, the proposed robust MPC has a less computational burden and improves the equilibrium point attractivity compared with the max–min MPC and the equality terminal constraint-based MPC. To illustrate the superiority of the proposed strategy, the suggested robust MPC is applied to a truck–trailer system and a numerical example. The simulation results show the capabilities of the proposed robust MPC.