Efficient Robust Fuzzy Model Predictive Control of Discrete Nonlinear Time-Delay Systems via Razumikhin Approach

Abstract

In this paper, two efficient robust fuzzy model predictive control algorithms are investigated for discrete nonlinear systems with multiple time delays and bounded disturbances. The famous Takagi–Sugeno (T–S) fuzzy systems are utilized to represent nonlinear systems. Instead of the Lyapunov–Krasovskii functional, the Lyapunov–Razumikhin function is adopted to deal with time delays because it involves invariant sets in the original state space of the system. A sequence of explicit control laws corresponding to a sequence of constraint sets are computed offline so that the online computational burden associated with the classical model predictive control algorithms is significantly reduced. In particular, the set invariance theory behind the Razumikhin approach, which is more complicated than the one for nondelayed systems, is directly observed. Additionally, it is proved that all (delayed) states can enter the terminal set in finite time. Moreover, robust positive invariance and input-to-state stability for time-delay systems concerning disturbances are realized. Additionally, an online optimization algorithm is also provided based on the offline computed ellipsoidal sets. Therefore, the conservatism induced by the Razumikhin approach is relaxed, while the computational cost is not significantly increased.