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On a Class of Hybrid Differential Games

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Abstract

This paper is intended to present a systematic application of the hybrid systems framework to differential games. A special class of bimodal linear-quadratic differential games is presented and illustrated with examples; two particular classes of switching rules, time-dependent and state-dependent switches are discussed. The main contribution of the paper consists in formulating necessary optimality conditions for determining optimal strategies in both cooperative and non-cooperative cases. A practically relevant hybrid differential game of pollution reduction is considered to illustrate the developed framework.

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Notes

  1. Obviously, in the case of minimization the respective matrices must be nonnegative and positive definite.

  2. Here and forth we will use standard notation: x(t) for the state, u(t) for the control and so on. This may contradict the established practice but will allow us to consider various problems in a uniform setting.

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Authors and Affiliations

  1. Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, St. Petersburg, Russia

    Dmitry Gromov & Ekaterina Gromova

Authors
  1. Dmitry Gromov
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  2. Ekaterina Gromova
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Correspondence to Dmitry Gromov.

Additional information

D. Gromov acknowledges the Grants 9.50.1197.2014 and 9.41.721.2015 from St. Petersburg State University, E. Gromova acknowledges the Grant 9.38.245.2014 from St. Petersburg State University.

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Gromov, D., Gromova, E. On a Class of Hybrid Differential Games. Dyn Games Appl 7, 266–288 (2017). https://doi.org/10.1007/s13235-016-0185-3

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