Model predictive control with implicit terminal ingredients

Abstract

This paper proposes a new formulation of model predictive control for linear discrete time systems under state and control constraints. The main novelty of the proposed formulation is the introduction, and a computationally adequate utilization, of the implicit terminal constraint set and the implicit terminal cost function. From a numerical point of view, the deployment of the implicit terminal ingredients enables a computationally tractable use of model predictive control for higher dimensional control problems. From a practical point of view, the design of the proposed model predictive control algorithm is very constructive for a class of linear systems with polyhedral constraints. From a structural point of view, the proposed model predictive control retains a priori guarantees of the highly desirable positive invariance and exponential stability properties.