Simplified Design of Practically Stable MPC Schemes

COMELLI, ROMAN; GONZÁLEZ, ALEJANDRO HERNÁN; FERRAMOSCA, ANTONIO; OLARU, SORIN; SERON, MARIA MARTA; KOFMAN, ERNESTO

SYSTEMS AND CONTROL LETTERS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2023

0167-6911

This work introduces a novel and simple way of designing MPC schemesthat ensure practical stability under less restrictive assumptions than thoseof existing approaches. The terminal control invariant set required by moststabilizing MPC formulations is replaced by a pair of simpler inner and outersets, which are not invariant but satisfy a weaker condition. The advantageof using this pair of sets instead of a classical invariant set is the flexibilityin their design and ultimately the simplicity. Two key modifications areintroduced in the optimal control problem that MPC solves at each time:(i) a constraint is added for the predicted state trajectory to have at leastone point of intersection with the inner set, and (ii) the stage cost function ismodified to account for the set membership of the state to the outer set, whichis the target region. It is shown that convergence to this target set is ensuredwithin finite-time and that the proposed MPC scheme can keep controllingthe system in the target set without requiring a different local controller. A numerical example with a nonlinear model of an inverted pendulum is usedto illustrate these results.