Abstract
This paper provides a decomposition technique for the purpose of simplifying the solution of certain zero-sum differential games. The games considered terminate when the state reaches a target, which can be expressed as the union of a collection of target subsets considered as ‘multiple targets’; the decomposition consists in replacing the original target by each of the target subsets. The value of the original game is then obtained as the lower envelope of the values of the collection of games, resulting from the decomposition, which can be much easier to solve than the original game. Criteria are given for the validity of the decomposition. The paper includes examples, illustrating the application of the technique to pursuit/evasion games and to flow control.
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This research was supported by the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN SADCO, ‘Sensitivity Analysis for Deterministic Controller Design’.
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Festa, A., Vinter, R.B. Decomposition of Differential Games with Multiple Targets. J Optim Theory Appl 169, 848–875 (2016). https://doi.org/10.1007/s10957-016-0908-z
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DOI: https://doi.org/10.1007/s10957-016-0908-z