A New Contraction-Based NMPC Formulation Without Stability-Related terminal Constraints

Abstract: Contraction-Based Nonlinear Model Predictive Control (NMPC) formulations are attractive because of the generally short prediction horizons they require and the needless use of terminal set computation that are commonly necessary to guarantee stability. However, the inclusion of the contraction constraint in the definition of the underlying optimization problem often leads to non standard features such as the need for multi-step open-loop application of control sequences or the use of multi-step memorization of the contraction level that may induce unfeasibility in presence of unexpected disturbance. This paper proposes a new formulation of contraction-based NMPC in which no contraction constraint is explicitly involved. Convergence of the resulting closed-loop behavior is proved under mild assumptions.