Efficient Fuzzy Model Predictive Tracking Control of Nonlinear Systems: A Membership Function Approximation Approach

This article investigates the model predictive tracking control problem for nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. First, in order to alleviate the online computational burden of the MPC algorithm, a simplified model-based predictive strategy is developed, where the nominal system is approximated by a known linear time-varying (LTV) model, enabling the online optimization to be formulated as a quadratic programming (QP) problem. Thereafter, to ensure recursive feasibility and bounded tracking errors under fuzzy approximation errors and bounded disturbances, a Lyapunov-based dynamically updated tracking error constraint is introduced. Furthermore, by converting the original ellipsoidal constraints into relaxed box constraints, computational complexity is further reduced without violating the Lyapunov-based guarantees, which is ensured by an auxiliary one-step optimizer incorporated in the online part of the proposed framework. Compared with existing results, the proposed approach maintains bounded tracking errors with relatively high computational efficiency. The effectiveness of the proposed MPC framework is then demonstrated through simulation results.