Contraction-based nonlinear model predictive control formulation without stability-related terminal constraints

Contraction-based nonlinear model predictive control (NMPC) formulations are attractive because they generally require short prediction horizons, and there is no need for the terminal set computation and reinforcement that are common requirements 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 a need for the multi-step open-loop application of control sequences or the use of multi-step memorization of the contraction level, which may cause unfeasibility in the presence of unexpected disturbances. In this study, we propose a new contraction-based NMPC formulation where no contraction constraint is explicitly involved. The convergence of the resulting closed-loop behavior is proved under mild assumptions. An illustrative example is provided in order to demonstrate the relevance of the proposed formulation.