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Controllability Properties of Linear Mean-Field Stochastic Systems

Dan Goreac 1
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : We study some controllability properties for linear stochastic systems of mean-fi…eld type. First, we give necessary and sufficient criteria for exact terminal-controllability. Second, we characterize the approximate and approximate null-controllability via duality techniques. Using Riccati equations associated to linear quadratic problems in the control of mean-…field systems, we provide a (conditional) viability criterion for approximate null-controllability. In the classical diffusion framework, approximate and approximate null-controllability are equivalent. This is no longer the case for mean-fi…eld systems. We provide sufficient (algebraic) invariance conditions implying approximate null-controllability. We also present a general class of systems for which our criterion is equivalent to approximate null-controllability property. We also introduce some rank conditions under which approximate and approximate null-controllability are equivalent. Several examples and counter-examples as well as a partial algorithm are provided.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00879277
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Submitted on : Saturday, November 2, 2013 - 1:57:41 PM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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Dan Goreac. Controllability Properties of Linear Mean-Field Stochastic Systems. Stochastic Analysis and Applications, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2014, 32 (2), pp.280 - 297. ⟨10.1080/07362994.2013.862637⟩. ⟨hal-00879277⟩

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