Fuzzy Model Predictive Control of Discrete-Time Systems with Time-Varying Delay and Disturbances

In this paper, model predictive control (MPC) of discrete T–S fuzzy systems subjected to bounded time-varying delay and persistent disturbances is investigated. The Razumikhin approach is adopted for time-delay systems because it involves a Lyapunov function associated with the original nonaugmented state space of system dynamics when compared to the Krasovskii approach. As such, the Razumikhin approach has a good potential to avoid the inherent complexity of the Krasovskii approach especially in the presence of large delays and disturbances. Based on which, both online and offline MPC approaches for systems with time-varying delay are provided. In addition, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are realized. In the offline approach, a sequence of explicit control laws that correspond to a sequence of robust constraints sets are computed offline. And it is proved that system states including all possibly delayed states can be steered to the terminal constraint set in finite time. Moreover, it allows the exact time delay to be unknown in the proposed two approaches. In particular, for systems with time-varying delay, the special positively invariant set theory and finite-time control theory based on the Razumikhin approach are directly revealed via the proposed offline approach.