Set-Valued Model Predictive Control

Model predictive control (MPC) is a valuable tool to deal with systems that require optimal solutions and constraint satisfaction. In the case of systems with uncertainty, the formulation of predictive controllers requires models which are capable to capture system dynamics, constraints and also system uncertainty. In this work we present a formulation for a set-valued model predictive control (SVMPC) where uncertainty is represented in terms of sets. The approach presented here considers a model where the state is set-valued and dynamics are defined by a set-valued map. The cost function associated to the proposed MPC associates a real-valued cost to each set valued (or tube-based) trajectory. For this formulation, we study conditions that can yield the constrained optimal control problem associated to the set-valued MPC formulation feasible and stable, thus extending existing stability results from classic MPC to a set-based approach. Examples illustrate the results along the paper.