Receding horizon predictive control for linear time-delay systems

A general receding horizon predictive control (RHPC), or model predictive control (MPC), for time-delay systems is proposed. The proposed RHPC is obtained by minimizing a new cost that includes two terminal weighting terms, which are closely related to the closed-loop stability. The general solution of the proposed RHPC is derived using the generalized Riccati method. Furthermore, an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size. A linear matrix inequality (LMI) condition on the terminal weighting matrices is proposed, under which the optimal cost is guaranteed to be monotonically non-increasing. It is shown that the monotonic condition of the optimal cost guarantees closed-loop stability of the RHPC. Simulations demonstrate that the proposed RHPC effectively stabilizes time-delay systems.