Model predictive control of constrained non-linear time-delay systems

This paper proposes a model predictive control scheme for non-linear time-delay systems with input constraints. Based on the results for systems without delays, asymptotic stability of the closed loop is guaranteed by utilizing an appropriate terminal cost functional and an appropriate terminal region such that the optimal cost for the finite-horizon problem is an upper bound on the optimal cost for the associated infinite-horizon problem. Two structured procedures are presented to determine offline the terminal cost and the terminal region for a class of non-linear time-delay systems. For both procedures, sufficient conditions can be formulated in terms of linear matrix inequalities based on the Jacobi linearization of the system about the origin. The first procedure uses a combination of Lyapunov–Krasovskii and Lyapunov–Razumikhin conditions in order to compute a locally stabilizing controller and a control invariant region. The second procedure only applies Lyapunov–Krasovskii arguments but may yield more complicated control invariant regions. The effectiveness of both schemes is compared for the example of a continuous stirred tank reactor with recycle stream.