Reduced-complexity interpolating control with periodic invariant sets

Scialanga, S., Olaru, S. and Ampountolas, K. (2023) Reduced-complexity interpolating control with periodic invariant sets. International Journal of Control, 96(3), pp. 757-769. (doi: 10.1080/00207179.2021.2013540)

Abstract

This paper deals with the constrained control of linear systems and presents a low-complexity interpolating control scheme based on the concept of periodic invariance. Periodic invariance avoids the expensive computation of the control invariant set and allows the state trajectory to leave the set temporarily but return into the set in a finite number of steps, i.e. period of the invariant set, all by satisfying the constraints. Furthermore, periodic invariant sets provide a reduction of complexity representation by replacing the classical control invariant set. In practice, a reachability problem is solved off-line for each vertex of the set and provides a contractive control sequence that steers the system state back into the original set (vertex reachability of target sets). Online, the periodic interpolating control (pIC) scheme allows to transition between such periodic invariant sets and a inner set endorsed with positive invariance properties. Proofs of recursive feasibility and asymptotic stability of the pIC are given. A numerical example demonstrates that pIC provides similar performance compared to more expensive optimization-based schemes.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ampountolas, Dr Konstantinos and Scialanga, Sheila
• Authors: Scialanga, S., Olaru, S., and Ampountolas, K.
• College/School: College of Science and Engineering > School of Engineering
• Journal Name: International Journal of Control
• Publisher: Taylor and Francis
• ISSN: 0020-7179
• ISSN (Online): 1366-5820
• Published Online: 01 December 2021
• Copyright Holders: Copyright © 2021 Informa UK Limited, trading as Taylor and Francis Group
• First Published: First published in International Journal of Control 96(3): 757-769
• Publisher Policy: Reproduced in accordance with the publisher copyright policy