On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems
| Autor: | Laurent Pfeiffer, Tobias Breiten |
|---|---|
| Přispěvatelé: | University of Graz, Controle, Optimisation, modèles, Méthodes et Applications pour les Systèmes Dynamiques non linéaires (COMMANDS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Karl-Franzens-Universität Graz, Karl-Franzens-Universität [Graz, Autriche] |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization Control and Optimization Property (programming) model predictive control Time horizon 02 engineering and technology 01 natural sciences Riccati equation 020901 industrial engineering & automation Bellman equation FOS: Mathematics optimality systems 0101 mathematics [MATH]Mathematics [math] Mathematics - Optimization and Control 49J20 49L20 49Q12 93D15 Mathematics Sequence Horizon (archaeology) Applied Mathematics 010102 general mathematics Receding horizon control Optimal control value function Model predictive control Optimization and Control (math.OC) turnpike property AMS subject classifications. 49J20 |
| Zdroj: | SIAM Journal on Control and Optimization SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, 58 (2), pp.26. ⟨10.1137/18M1225811⟩ SIAM Journal on Control and Optimization, 2020, 58 (2), pp.26. ⟨10.1137/18M1225811⟩ |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.1137/18M1225811⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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