A Soft Constrained MPC Formulation Enabling Learning From Trajectories With Constraint Violations

Abstract

In practical model predictive control (MPC) implementations, constraints on the states are typically softened to ensure feasibility despite unmodeled disturbances. In this work, we propose a soft constrained MPC formulation supporting polytopic terminal sets in half-space and vertex representation, which significantly increases the feasible set while maintaining asymptotic stability in case of constraint violations. The proposed formulation allows for leveraging system trajectories that violate state constraints to iteratively improve the MPC controller's performance. To this end, we apply convex optimization techniques to obtain a data-driven terminal cost and set, which result in a quadratic MPC problem.