Slow Decay and Turnpike for Infinite-Horizon Hyperbolic Linear Quadratic Problems
Abstract
This paper is devoted to analyzing the explicit slow decay rate and turnpike in infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Under suitable weak observability or controllability conditions, lower and upper bounds of the corresponding algebraic Riccati operator are proved. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to LQ optimal control problems constrained to networks of one-dimensional wave equations and also some multidimensional ones with local controls which lack a geometric control condition.
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Information & Authors
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Published In
SIAM Journal on Control and Optimization
Pages: 2440 - 2468
DOI: 10.1137/21M1441985
ISSN (online): 1095-7138
Copyright
© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 24 August 2021
Accepted: 13 May 2022
Published online: 16 August 2022
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Alexander von Humboldt-Stiftung https://doi.org/10.13039/100005156
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Deutsche Forschungsgemeinschaft https://doi.org/10.13039/501100001659
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H2020 Marie Skłodowska-Curie Actions https://doi.org/10.13039/100010665 : 765579-ConFlex
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Horizon 2020 Framework Programme https://doi.org/10.13039/100010661 : 694126-DyCon
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Ministerio de Economía, Industria y Competitividad, Gobierno de España https://doi.org/10.13039/501100010198 : MTM2017-92996-C2- 1-R COSNET
Funding Information
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : NSFC-62073236
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