Output Feedback Model Predictive Control of Interval Type-2 T–S Fuzzy System With Bounded Disturbance

Abstract

In this paper, the problem of output feedback model predictive control (MPC) for interval Type-2 Takagi–Sugeno fuzzy systems with bounded disturbance is investigated. The output feedback MPC approach includes an offline design of the state observer to estimate true states and predict bounds of future estimation error sets, and an online problem that optimizes the controller gains to stabilize the closed-loop observer system. The dynamics of the estimation error system is determined by the offline designed observer gain, and bounds of which are online refreshed by scaling a minimal robust positively invariant (RPI) set via a scalar. The optimized controller gains steer the current estimated state from an RPI set into another one such that future estimated states are invariant in the subsequent RPI set. Convergence of the estimation error system and stability condition on the closed-loop observer system in terms of linear matrix inequalities are derived using the technique of S-procedure. The estimation error and estimated state converge within the corresponding time-varying RPI sets, and therefore, recursive feasibility of the optimization problem and input-to-state stability of the closed-loop observer system with respect to the estimation error and bounded disturbance are ensured. For reducing the online computational burden, a lookup table that stores the offline calculated controller gains with corresponding regions of attraction is offline constructed for online searching real-time controller gains. A simulation example is given to show the effectiveness of the approach.