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Measure-Driven Nonlinear Dynamic Systems with Applications to Optimal Impulsive Controls

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Abstract

In this paper, we consider a class of nonlinear systems driven by measures generalizing the class of impulsive systems. We use measures as control and prove existence of optimal controls (measures) and present necessary conditions of optimality. We apply the general results to derive necessary conditions of optimality for purely impulse-driven systems. These results are then applied to optimal control problems related to geosynchronous satellites with some numerical results.

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Acknowledgements

The authors would like to thank the anonymous reviewers for many critical comments and suggestions which led to significant improvement in the manuscript.

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Author notes

  1. Shian Wang

    Present address: University of Minnesota, Minneapolis, MN, USA

Authors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Nasir Uddin Ahmed & Shian Wang

Authors
  1. Nasir Uddin Ahmed
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  2. Shian Wang
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Correspondence to Nasir Uddin Ahmed.

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Communicated by Emmanuel Trelat.

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Ahmed, N.U., Wang, S. Measure-Driven Nonlinear Dynamic Systems with Applications to Optimal Impulsive Controls. J Optim Theory Appl 188, 26–51 (2021). https://doi.org/10.1007/s10957-020-01769-9

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  • DOI: https://doi.org/10.1007/s10957-020-01769-9

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