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Approximately Reachable Directions for Piecewise Linear Switched Systems

Dan Goreac 1
1 PS
LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
Abstract : This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0 (belong to the closure of the reachable set in a suitable L 2-sense). From a mathematical point of view, this provides the missing link between approximate controllability towards 0 and approximate controllability towards given targets. The methods rely on linear-quadratic control and Riccati equations. The main novelty is that we consider an LQ problem with controlled backward stochastic dynamics and, since the coefficients are not deterministic (unlike some of the cited references), neither is the backward stochastic Riccati equation. Existence and uniqueness of the solution of such equations rely on structure arguments (inspired by [7]). Besides solvability, Riccati representation of the resulting control problem is provided as is the synthesis of optimal (non-Markovian) control. Several examples are discussed.
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Submitted on : Thursday, October 25, 2018 - 12:34:32 PM
Last modification on : Friday, November 20, 2020 - 3:01:49 PM
Long-term archiving on: : Saturday, January 26, 2019 - 2:03:58 PM

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Dan Goreac. Approximately Reachable Directions for Piecewise Linear Switched Systems. Mathematics of Control, Signals, and Systems, Springer Verlag, 2019, 31 (31), pp.333-362. ⟨10.1007/s00498-019-0240-x⟩. ⟨hal-01831465v2⟩

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