Relaxed Model Predictive Control of T-S Fuzzy Systems via a New Switching-Type Homogeneous Polynomial Technique

This paper proposes a novel approach to model predictive control (MPC) for Takagi-Sugeno (T-S) fuzzy systems by combining the homogeneous polynomial technique and a switching mechanism. Aiming at improving the overall system performance by dynamically switching between different controllers according to system dynamics changing, the proposed switching MPC (SMPC) scheme formulates a group of optimization problems to determine the optimal switching strategy and corresponding control actions. To be specific, the optimization problem is solved at each moment to generate a control sequence that optimizes the gain matrices to achieve the minimized performance index. Building upon the traditional MPC structure, the proposed SMPC method forms a new framework by reducing the conservatism of controller design in the solving process based on linear matrix inequality (LMI) conditions via introducing the homogeneous polynomial method. As a result, the proposed SMPC method enhances the feasibility of controller solving, improves control performance and expands the domain of attraction by utilizing the switching mechanism to handle the system dynamics more freely. Finally, the effectiveness and superiority of the proposed method are validated through different examples.