Observer-based H∞Model Predictive Control for Nonlinear Discrete-time Systems with Bounded Disturbance

Abstract This study introduces an observer-based H∞ model predictive control strategy, designed for discrete-time nonlinear systems affected by bounded disturbances. Initially, an output-feedback control strategy is utilized to parameterize control actions over an infinite interval and to estimate the system state. This strategy is integrated into model predictive control (MPC) to achieve optimal control and state tracking within the closed-loop system. Subsequently, the Takagi-Sugeno (T-S) fuzzy logic model is employed to address the nonlinear terms of the system, and the H∞ performance index is used to mitigate the adverse effects of bounded disturbances on system output. With the assistance of Lyapunov stability theory and linear matrix inequalities (LMI) optimization method, sufficient conditions to ensure the system's asymptotic convergence are provided. To demonstrate the effectiveness of the proposed method, a numerical example and an engineering application example are presented.