Controllability Properties of Linear Mean-Field Stochastic Systems |
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Authors: | DAN Goreac |
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Institution: | 1. Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS , Marne-la-Valle , France dan.goreac@univ-mlv.fr |
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Abstract: | We study some controllability properties for linear stochastic systems of mean-field 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-field 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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Keywords: | Controllability invariance Mean-field linear stochastic systems Riccati equation |
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