Finding the LQR weights to ensure the associated Riccati equations admit a common solution

Lan, J. and Zhao, D. (2023) Finding the LQR weights to ensure the associated Riccati equations admit a common solution. IEEE Transactions on Automatic Control, 68(10), pp. 6393-6400. (doi: 10.1109/TAC.2023.3234237)

Abstract

This paper addresses the problem of finding the linear quadratic regulator (LQR) weights such that the associated discrete-time algebraic Riccati equations admit a common optimal stabilising solution. Solving such a problem is key to designing LQR controllers to stabilise discrete-time switched linear systems under arbitrary switching, or stabilise polytopic systems (e.g., Takagi-Sugeno fuzzy systems and linear parameter varying systems) in the entire operating region. To ensure problem tractability and reduce the searching space, this paper proposes an efficient framework of finding only the state weights based on the given input weights. Linear matrix inequality conditions are derived to conveniently check feasibility of the problem. An iterative algorithm with quadratic convergence and low computational complexity is developed to solve the problem. Efficacy of the proposed method is illustrated through numerical simulations of systems with various sizes.

• Item Type: Articles
• Additional Information: Jianglin Lan was supported by a Leverhulme Trust Early Career Fellowship under Award ECF-2021-517. Dezong Zhao was supported by the Engineering and Physical Sciences Research Council of UK under the EPSRC-UKRI Innovation Fellowship scheme (EP/S001956/1).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Zhao, Dr Dezong and Lan, Dr Jianglin
• Authors: Lan, J., and Zhao, D.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Journal Name: IEEE Transactions on Automatic Control
• Publisher: IEEE
• ISSN: 0018-9286
• ISSN (Online): 1558-2523
• Published Online: 04 January 2023
• Copyright Holders: Copyright © 2023 IEEE
• First Published: First published in IEEE Transactions on Automatic Control 68(10): 6393-6400
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
314774		Toward Energy Efficient Autonomous Vehiciles via Cloud-Aided learning	Dezong Zhao	Engineering and Physical Sciences Research Council (EPSRC)	EP/S001956/2	ENG - Autonomous Systems & Connectivity