J Optim Theory Appl https://doi.org/10.1007/s10957-018-1313-6 Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations 1 2,3 JinRong Wang · Michal Feckan ˇ · Amar Debbouche Received: 6 October 2017 / Accepted: 15 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We investigate time optimal control of a system governed by a class of non-instantaneous impulsive differential equations in Banach spaces. We use an appro- priate linear transformation technique to transfer the original impulsive system into an approximate one, and then we prove the existence and uniqueness of their mild solutions. Moreover, we show the existence of optimal controls for Meyer problems of the approximate. Further, in order to solve the time optimal control problem for the original system, we construct a sequence of Meyer approximations for which the desired optimal control and optimal time are well derived. Keywords Non-instantaneous impulsive differential equations · Time optimal controls · Meyer approximation approach Communicated by Irena Lasiecka. B JinRong Wang email@example.com Michal Feckan ˇ Michal.Feckan@fmph.uniba.sk Amar Debbouche firstname.lastname@example.org Department of Mathematics, Guizhou University, Guiyang 550025, Guizhou, People’s Republic of China Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius
Journal of Optimization Theory and Applications – Springer Journals
Published: Jun 4, 2018
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