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)

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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).
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
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

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
314774Toward Energy Efficient Autonomous Vehiciles via Cloud-Aided learningDezong ZhaoEngineering and Physical Sciences Research Council (EPSRC)EP/S001956/2ENG - Autonomous Systems & Connectivity