Separation principle in the fractional Gaussian linear-quadratic regulator problem with partial observation
| Autor: | M. Viot, Alain Le Breton, Marina Kleptsyna |
|---|---|
| Přispěvatelé: | Département de Mathématiques [Le Mans], Le Mans Université (UM), Statistique et Modélisation Stochatisque (SMS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2008 |
| Předmět: |
Statistics and Probability
Gaussian quadratic payoff Linear-quadratic regulator Separation principle Linear-quadratic-Gaussian control 01 natural sciences Fractional Brownian motion 010104 statistics & probability symbols.namesake optimal control Quadratic equation Control theory [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Applied mathematics linear system MSC: 93E11 93E20 60G15 60G44 0101 mathematics Mathematics 010102 general mathematics Linear system optimal filtering [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Optimal control separation principle symbols |
| Zdroj: | ESAIM: Probability and Statistics ESAIM: Probability and Statistics, EDP Sciences, 2008, 12, pp.94-126. ⟨10.1051/ps:2007046⟩ |
| ISSN: | 1292-8100 1262-3318 |
| DOI: | 10.1051/ps:2007046⟩ |
| Popis: | International audience; In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we show that a separation principle holds, i.e., the optimal control separates into two stages based on optimal filtering of the unobservable state and optimal control of the filtered state. Both finite and infinite time horizon problems are investigated. |
| Databáze: | OpenAIRE |
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