On Stability of Constrained Receding Horizon Control with Finite Terminal Weighting Matrix

Authors:
JAE-WON LEE;WOOK HYUN KWON;JINHOON CHOI
Affiliations:
Systems and Control Sector, Samsung Advanced Institute of Technology, Suwon, P.O. Box 111, South Korea;School of Electrical Engineering, Seoul National University, Seoul, South Korea;Department of Chemical Engineering, Sogang University, South Korea
Venue:
Automatica (Journal of IFAC)
Year:
1998

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Abstract

In this paper, a new stabilizing receding horizon control, based on a finite input and state horizon cost with a finite terminal weighting matrix, is proposed for time-varying discrete linear systems with constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed-loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints. We show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality (LMI). In the case of constrained time-invariant systems, an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control.