Geodesic
Nonequivalence of Controllability Properties for Piecewise Linear Markov Switch Processes
Dan Goreac1
1 Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France,
ESAIM. Proceedings, Tome 57 (2017), pp. 37-47.

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In this paper we study the exact null-controllability property for a class of controlled PDMP of switch type with switch-dependent, piecewise linear dynamics and multiplicative jumps. First, we show that exact null-controllability induces a controllability metric. This metric is linked to a class of backward stochastic Riccati equations. Using arguments similar to the euclidian-valued BSDE in [4], the equation is shown to be equivalent to an iterative family of deterministic Riccati equations that are solvable. Second, we give an example showing that, for switch-dependent coefficients, exact null-controllability is strictly stronger than approximate null-controllability. Finally, we show by convenient examples that no hierarchy holds between approximate (full) controllability and exact null-controllability. The paper is intended as a complement to [11] and [10].
DOI : 10.1051/proc/201657037

Dan Goreac 1

1 Université Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, F-77454, Marne-la-Vallée, France, 
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Dan Goreac. Nonequivalence of Controllability Properties for Piecewise Linear Markov Switch Processes. ESAIM. Proceedings, Tome 57 (2017), pp. 37-47. doi : 10.1051/proc/201657037. http://geodesic.mathdoc.fr/articles/10.1051/proc/201657037/

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