Simplified design of practically stable MPC schemes

Abstract

This work introduces a novel and simple way of designing MPC schemes that ensure practical stability under less restrictive assumptions than those of existing approaches. The terminal control invariant set required by most stabilizing MPC formulations is replaced by a pair of simpler inner and outer sets, which are not invariant but satisfy a weaker condition. The advantage of using this pair of sets instead of a classical invariant set is the flexibility in their design and ultimately the simplicity. Two key modifications, one in the stage cost function and other related to a constraint, are introduced in the optimal control problem that MPC solves at each time. It is shown that convergence to the outer set, which is the target region, is ensured within finite-time and that the proposed MPC scheme can keep controlling the system in the target set without requiring a different local controller. A numerical example with a nonlinear model of an inverted pendulum is used to illustrate these results.