Data-driven Model Predictive Control of Time-delay Systems

This letter investigates a data-driven model predictive control (MPC) scheme for time-delay systems with unknown dynamics as well as input and state constraints. An infinite-horizon optimization problem is first formulated, in which a data-driven system representation is employed as a predictive model, and a delay-dependent state feedback controller is designed. By introducing a Lyapunov function, the control problem is systematically reduced to a tractable form, with a sufficient condition for the controller existence derived based on linear matrix inequality techniques. Then, the recursive feasibility of the MPC optimization and the stability of the resulting closed-loop system are rigorously established. Finally, the effectiveness of the proposed method is verified through numerical simulation.