Receding Horizon Control for Input-Delayed Systems

We propose the receding horizon control (RHHC) for input-delayed systems. A new cost function for a finite horizon dynamic game problem is first introduced, which includes two terminal weighting terms parameterized by a positive definite matrix, called a terminal weighing matrix. Secondly, the RHHC is obtained from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and boundedness of the closed-loop system controlled by the proposed RHHC. The proposed RHHC has a guaranteed performance bound for nonzero external disturbances and the quadratic cost can be improved by adjusting the prediction horizon length for nonzero initial condition and zero disturbance, which is not the case for existing memoryless state-feedback controllers. It is shown through a numerical example that the proposed RHHC is stabilizing and satisfies the infinite horizon performance bound. Furthermore, the performance in terms of the quadratic cost is shown to be improved by adjusting the prediction horizon length when there exists no external disturbance with nonzero initial condition.