Robust Fuzzy Model Predictive Control with time delays for Nonlinear Systems

Abstract

In this work, a robust fuzzy model predictive control (RFMPC) is designed for uncertain time-delay systems under input constraints with external disturbances. The proposed controller is based on an augmented state space model that includes the state variables and output tracking error variable of system. As a result, the proposed control based on augmented state space model can guarantee the convergence and tracking performance of system. To ensure the stability of the closed loop constrained time-delays system, in the form of linear matrix inequalities (LMIs), the Lyapunov–Krasovskii (L-K) theory is employed to derive sufficient stability conditions where the L-K theory has the ability to reflect the system’s original state space and its advantages in controller synthesis and computation. As a result, less conservative stable conditions in terms of LMIs are given and used to ensure the asymptotically robust stability of closed-loop constrained system, and the controller construction procedure in shifted into a minimization problem subjected to certain constraints in terms of LMI. The robustness properties of the proposed RFMPC approach are compared with the results of a standard predictive control MPC applied to control a nonlinear system with parameter uncertainties and time-delays.