Robust Model Predictive Control for Discrete-Time Takagi–Sugeno Fuzzy Systems With Structured Uncertainties and Persistent Disturbances

In this paper, robust model predictive control for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with input constraints and persistent disturbances is considered. The robust positively invariant set for T-S fuzzy systems is investigated. Based on this result, computation of the terminal constraint set is proposed, which is of crucial importance in the robust predictive controller design. A zero-step predictive controller is discussed first, which has a time-varying terminal constraint set. The recursive feasibility and input-to-state stability can be ensured. Then, a novel controller with N-step prediction is further proposed, which can be used to deal with the case of fixed terminal constraint set. The implementation of the N-step controller involves both online and offline computations. It is shown that a sequence of approximating robust one-step sets can be computed offline. Then, bisection searches are carried out online, as well as a constrained convex optimization problem. The N-step controller guarantees that the system state can be steered to the terminal constraint set in less than N-steps, if the initial state lies in a specific region. Simulation results are finally presented to show the effectiveness of the proposed controllers.