Stability of NMPC with cyclic horizons

Abstract

In this paper we present stability conditions for nonlinear model predictive control with cyclically varying horizons. Starting from a maximum horizon length, the horizon is reduced by one at each sampling time until a minimum horizon length is reached, at which the horizon is increased to the maximum length. The approach allows to utilize shapes and structures in the terminal constraints, which can otherwise not be handled. Examples are terminal box-constraints, where the terminal set cannot be rendered invariant, or quadratic terminal regions and penalties of diagonal structure. Such constraints are for example of advantage for distributed predictive control problems. To underline the applicability, the approach is used to control a four tank system.