Optimal control of      dynamical systems  with polynomial impulses

Elena Goncharova; Maxim Staritsyn

doi:10.3934/dcds.2015.35.4367

Article Contents

2015, Volume 35, Issue 9: 4367-4384. Doi: 10.3934/dcds.2015.35.4367

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Optimal control of dynamical systems with polynomial impulses

Elena Goncharova^1, and
Maxim Staritsyn^1,

1.
Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk

Received: April 2014

Revised: September 2014

Published: May 2017

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Abstract

The paper is devoted to the $BV$-relaxation of a dynamical system, whose right-hand side is a $p$th degree polynomial with rational powers of control under a uniform bound on its $L_p$-norm, and coefficients containing usual measurable bounded control.
Under natural convexity assumptions, we give an explicit representation of generalized solutions to the control system by a measure differential equation. The main results concern an optimal impulsive control problem for the relaxed system: We establish the existence of a minimizer, and give necessary optimality conditions in the form of a Maximum Principle.

Keywords:

Mathematics Subject Classification: Primary: 49N25, 49K99; Secondary: 49J99.

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