Steady-state and periodic exponential turnpike property for optimal control problems in hilbert spaces
Entity
UAM. Departamento de MatemáticasPublisher
Society for Industrial and Applied MathematicsDate
2018-03-29Citation
10.1137/16M1097638
SIAM Journal on Control and Optimization 56.2 (2018): 1222-1252
ISSN
1095-7138 (online); 0363-0129 (print)DOI
10.1137/16M1097638Funded by
The authors acknowledge the nancial support by the grant FA9550-14-1-0214 of the EOARD-AFOSR. The second author was partially supported by the National Natural Science Foundation of China under grants 11501424 and 11371285. The third author was partially supported by the Advanced Grant DYCON (Dynamic Control) of the European Research Council Executive Agency, FA9550-15-1-0027 of AFOSR, the MTM2014-52347 and MTM2017-92996 grants of the MINECO (Spain), and ICON of the French ANRProject
Gobierno de España. MTM2014-52347; Gobierno de España. MTM2017-92996; info:eu-repo/grantAgreement/EC/H2020/694126/EU//DYCONEditor's Version
https://doi.org/10.1137/16M1097638Subjects
Dichotomy transformation; Exponential turnpike property; Periodic optimal controls; Periodic tracking; Stability analysis; MatemáticasNote
First Published in SIAM Journal on Control and Optimization in Volume 56, Issue 2, 2018, Pages 1222-1252, published by the Society for Industrial and Applied Mathematics (SIAM)Rights
© 2018 Society for Industrial and Applied Mathematic. Unauthorized reproduction of this article is prohibitedAbstract
In this work, we study the steady-state (or periodic) exponential turnpike property of optimal control problems in Hilbert spaces. The turnpike property, which is essentially due to the hyperbolic feature of the Hamiltonian system resulting from the Pontryagin maximum principle, reects the fact that, in large control time horizons, the optimal state and control and adjoint state remain most of the time close to an optimal steady-state. A similar statement holds true as well when replacing an optimal steady-state by an optimal periodic trajectory. To establish the result, we design an appropriate dichotomy transformation, based on solutions of the algebraic Riccati and Lyapunov equations. We illustrate our results with examples including linear heat and wave equations with periodic tracking terms
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Google Scholar:Trélat, Emmanuel
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Zhang, Can
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Zuazua Iriondo, Enrique
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