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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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Corresponding author

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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