Design of terminal cost functionals and terminal regions for model predictive control of nonlinear time-delay systems

Abstract

In this work, we present results on model predictive control (MPC) for nonlinear time-delay systems. MPC is one of the few control methods which can deal effectively with constrained nonlinear time-delay systems. In order to guarantee stability of the closed-loop, a local control Lyapunov functional in a region around the origin is in general utilized as terminal cost. It is well-known for delayfree systems that a control Lyapunov function calculated for the Jacobi linearization about the origin can also be used as a terminal cost for the nonlinear system for an appropriately chosen terminal region. However, the infinite-dimensional nature of time-delay systems circumvents a straight-forward extension of those schemes to time-delay systems. We present two schemes for calculating stabilizing design parameters based on the Jacobi linearization of the nonlinear time-delay system. The two schemes are based on different assumptions and yield different types of terminal regions. We compare the properties and discuss advantages and disadvantages of both schemes. © 2012 Springer-Verlag GmbH Berlin Heidelberg.