Model Predictive Control for Nonlinear Time-Delay Systems without Terminal Constraint

In this work we present new results on model predictive control (MPC) for nonlinear time-delay systems. In the first part we derive a novel scheme for determining a suitable terminal cost and terminal region based on the Jacobi linearization of the nonlinear system. The main advantage of the proposed scheme compared to previous results is that the terminal region is defined as a sublevel of the terminal cost functional without any restrictive requirements on the sampling time of the MPC. Based on this result, we present an MPC scheme without terminal constraint in the second part. The result extends existing results for delay-free systems and guarantees asymptotic stability of the closed-loop. The main difficulty in the derivation is to show that the integral over the stage cost has a lower bound if the state is outside of a certain region. This is directly satisfied for delay-free finite-dimensional systems, but requires additional arguments for time-delay systems.