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Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations

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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 appropriate 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.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Number 11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006) and Unite Foundation of Guizhou Province ([2015]7640); the Slovak Research and Development Agency (Grant Number APVV-14-0378) and the Slovak Grant Agency VEGA (Grant Numbers 2/0153/16 and 1/0078/17).

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, People’s Republic of China

    JinRong Wang

  2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

  4. Department of Mathematics, Guelma University, Guelma, 24000, Algeria

    Amar Debbouche

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  1. JinRong Wang
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  2. Michal Fečkan
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  3. Amar Debbouche
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Correspondence to JinRong Wang.

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Communicated by Irena Lasiecka.

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Wang, J., Fečkan, M. & Debbouche, A. Time Optimal Control of a System Governed by Non-instantaneous Impulsive Differential Equations. J Optim Theory Appl 182, 573–587 (2019). https://doi.org/10.1007/s10957-018-1313-6

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  • DOI: https://doi.org/10.1007/s10957-018-1313-6

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