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Dynamic Games and Applications
Published in: Dynamic Games and Applications 2/2017

26-03-2016

On a Class of Hybrid Differential Games

Authors: Dmitry Gromov, Ekaterina Gromova

Published in: Dynamic Games and Applications | Issue 2/2017

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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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Footnotes
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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Metadata
Title
On a Class of Hybrid Differential Games
Authors
Dmitry Gromov
Ekaterina Gromova
Publication date
26-03-2016
Publisher
Springer US
Published in
Dynamic Games and Applications / Issue 2/2017
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI
https://doi.org/10.1007/s13235-016-0185-3

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