Steady-state and periodic exponential turnpike property for optimal control problems in hilbert spaces
Trelat E, Zhang C, Zuazua E (2018)
Publication Type: Journal article
Publication year: 2018
Journal
Book Volume: 56
Pages Range: 1222-1252
Journal Issue: 2
DOI: 10.1137/16M1097638
Abstract
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.
Authors with CRIS profile
Involved external institutions
Wuhan University
China (CN)
University of Paris 7 - Denis Diderot / Université Paris VII Denis Diderot
France (FR)
Universidad Autónoma de Madrid (UAM)
Spain (ES)
China (CN)
University of Paris 7 - Denis Diderot / Université Paris VII Denis Diderot
France (FR)
Universidad Autónoma de Madrid (UAM)
Spain (ES)
How to cite
APA:
Trelat, E., Zhang, C., & Zuazua, E. (2018). Steady-state and periodic exponential turnpike property for optimal control problems in hilbert spaces. SIAM Journal on Control and Optimization, 56(2), 1222-1252. https://dx.doi.org/10.1137/16M1097638
MLA:
Trelat, Emmanuel, Can Zhang, and Enrique Zuazua. "Steady-state and periodic exponential turnpike property for optimal control problems in hilbert spaces." SIAM Journal on Control and Optimization 56.2 (2018): 1222-1252.
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