General design parameters of model predictive control for nonlinear time-delay systems

This work presents new results on model predictive control (MPC) for nonlinear time-delay systems. In the first part, a general scheme is presented for calculating stabilizing design parameters based on the Jacobi linearization of the system. It is proven that for each system with stabilizable linearization there exist a quadratic terminal cost functional and a finite terminal region which guarantee asymptotic stability of the closed-loop. This allows the calculation of suitable design parameters for MPC based on any method available for the control of linear time-delay systems. In contrast to the delay-free case, the terminal region obtained is not characterized as sublevel set of the terminal cost functional. In the second part, a new type of terminal region is presented. Based on additional Lyapunov-Razumikhin conditions on the linear local controller it is shown that the terminal region can indeed be formulated as sublevel set of a particular terminal cost functional.