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 The Bulletin of Irkutsk State University. Series Mathematics, 2018, Volume 25, Pages 46–62 (Mi iigum345)

Feedback minimum principle for impulsive processes

V. A. Dykhta, O. N. Samsonyuk

Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russian Federation

Abstract: We consider an optimal impulsive control problem with a terminal functional and trajectories of bounded variation. The control system we consider has a bilinear structure with respect to the state and control variables and is governed by nonnegative vector Borel measures under constraints on their total variation. This problem is the impulsive-trajectory extension for the corresponding classical optimal control problem, which, in general, does not have optimal solutions with measurable controls. We do not posit any commutativity assumptions guaranteeing the well-posedness property for the impulsive extension. The so-called singular space-time transformation is used to define an individual trajectory and transform the impulsive system to an auxiliary ordinary control system.
The aim of this paper is to prove a nonlocal necessary optimality condition for impulsive processes. This condition is based on feedback controls providing descent directions for the functional. This necessary condition is called the feedback minimum principle. It is a generalization of the corresponding principle for classical optimal control problems. The feedback minimum principle is formulated within the framework of the generalized maximum principle for impulsive processes. An example illustrating the optimality condition is considered.

Keywords: impulsive control, trajectory of bounded variation, feedback control, optimality condition.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-01-00733_à

DOI: https://doi.org/10.26516/1997-7670.2018.25.46

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Document Type: Article
UDC: 517.977.5
MSC: 93C10, 93C23

Citation: V. A. Dykhta, O. N. Samsonyuk, “Feedback minimum principle for impulsive processes”, The Bulletin of Irkutsk State University. Series Mathematics, 25 (2018), 46–62

Citation in format AMSBIB
\Bibitem{DykSam18} \by V.~A.~Dykhta, O.~N.~Samsonyuk \paper Feedback minimum principle for impulsive processes \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2018 \vol 25 \pages 46--62 \mathnet{http://mi.mathnet.ru/iigum345} \crossref{https://doi.org/10.26516/1997-7670.2018.25.46} 

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