Nonlinear model predictive control based on K-step control invariant sets

Abstract

One of the fundamental issues in Nonlinear Model Predictive Control (NMPC) is to be able to guarantee the recursive feasibility of the underlying receding horizon optimization. In other terms, the primary condition for a safe NMPC design is to ensure that the closed-loop solution remains indefinitely within the feasible set of the optimization problem. This issue can be addressed by introducing a terminal constraint described in terms of a control invariant set. However, the control invariant sets of nonlinear systems are often impractical to use or even to construct due to their complexity. The $K$-step control invariant sets are representing generalizations of the classical one-step control invariant sets and prove to retain the useful properties for MPC design, but often with simpler representations, and thus greater applicability. In this paper, a novel NMPC scheme based on $K$-step control invariant sets is proposed. We employ symbolic control techniques to compute a $K$-step control invariant set and build the NMPC framework by integrating this set as a terminal constraint, thereby ensuring recursive feasibility.