Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control

Stepan Sorokin; Maxim Staritsyn

doi:10.3934/naco.2017014

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2017, Volume 7, Issue 2: 201-210. Doi: 10.3934/naco.2017014

This issue Previous Article Sufficient optimality conditions for extremal controls based on functional increment formulas Next Article Global optimization reduction of generalized Malfatti's problem

Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control

Stepan Sorokin^, and
Maxim Staritsyn

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences, 134, Lermontov St., 664033, Irkutsk, Russia

^* Corresponding author: Stepan Sorokin
^* Corresponding author: Stepan Sorokin

Received: November 30, 2016

Revised: April 30, 2017

Published: October 2017

This paper was prepared at the occasion of The 10th International Conference on Optimization: Techniques and Applications (ICOTA 2016), Ulaanbaatar, Mongolia, July 23-26,2016, with its Associate Editors of Numerical Algebra, Control and Optimization (NACO) being Prof. Dr. Zhiyou Wu, School of Mathematical Sciences, Chongqing Normal University, Chongqing, China, Prof. Dr. Changjun Yu, Department of Mathematics and Statistics, Curtin University, Perth, Australia, and Shanghai University, China, and Prof. Gerhard-Wilhelm Weber, Middle East Technical University, Ankara, Turkey.

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Abstract

We consider a class of rightpoint-constrained state-linear (but non convex) optimal control problems, which takes its origin in the impulsive control framework. The main issue is a strengthening of the Pontryagin Maximum Principle for the addressed problem. Towards this goal, we adapt the approach, based on feedback control variations due to V.A. Dykhta [4,5,6,7]. Our necessary optimality condition, named the feedback maximum principle, is expressed completely in terms of the classical Maximum Principle, but is shown to discard non-optimal extrema. As a connected result, we derive a certain form of duality for the considered problem, and propose the dual version of the proved necessary optimality condition.

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Mathematics Subject Classification: Primary: 49K15, 49K99; Secondary: 93C30.

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References

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