MPC for Sampled-Data Linear Systems: Guaranteeing Constraint Satisfaction in Continuous-Time

Author

Sopasakis, Pantelis ; Patrinos, Panagiotis ; Sarimveis, Haralambos

Author_Institution

IMT Inst. for Adv. Studies Lucca, Lucca, Italy

Volume

59

Issue

4

fYear

2014

fDate

Apr-14

Firstpage

1088

Lastpage

1093

Abstract

Model Predictive Controllers (MPC) designed for sampled-data systems can be shown to violate the constraints in continuous time. A reformulation of the initial problem will guarantee constraint satisfaction throughout the intersample period. Polytopic inclusions of the continuous trajectory are used in this technical note to establish additional constraints leading to a linearly constrained quadratic optimization problem. Continuous time asymptotic stability and continuous-time positive invariance are proven for the reformulated problem.

Keywords

approximation theory; asymptotic stability; constraint satisfaction problems; continuous time systems; control system synthesis; linear programming; linear systems; predictive control; quadratic programming; sampled data systems; MPC; constraint satisfaction; continuous time asymptotic stability; continuous trajectory; continuous-time positive invariance; intersample period; linearly constrained quadratic optimization problem; model predictive controllers; polytopic inclusions; polytopic overapproximation; reformulated problem; sampled-data linear systems; Asymptotic stability; Closed loop systems; Convergence; Optimization; Prediction algorithms; Predictive control; Trajectory; Continuous invariance; model predictive control; polytopic overapproximation; sampled data;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2285786

Filename

6632877