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On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems

Abstract : Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this article is the proof of the exponential convergence (with respect to the prediction horizon) of the control generated by the RHC method towards the exact solution of the problem. The result is established for a class of infinite-dimensional linear-quadratic optimal control problems with time-independent dynamics and integral cost. Such problems satisfy the turnpike property: the optimal trajectory remains most of the time very close to the solution to the associated static optimization problem. Specific terminal cost functions, derived from the Lagrange multiplier associated with the static optimization problem, are employed in the implementation of the RHC method.
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https://hal.inria.fr/hal-03113182
Contributor : Laurent Pfeiffer Connect in order to contact the contributor
Submitted on : Monday, January 18, 2021 - 10:58:38 AM
Last modification on : Friday, January 21, 2022 - 3:12:57 AM
Long-term archiving on: : Monday, April 19, 2021 - 6:39:41 PM

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Tobias Breiten, Laurent Pfeiffer. On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58 (2), pp.26. ⟨10.1137/18M1225811⟩. ⟨hal-03113182⟩

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