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Reach-Avoid Differential Games with Targets and Obstacles Depending on Controls

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Abstract

The reach-avoid differential game with targets and constraints which may also depend on the control functions is studied. The set of initial points which can steer the trajectory into a target while avoiding the constraints is characterized as the 0-sublevel set of the value function of such a game. This value function is characterized as the unique viscosity solution of a nonlinear variational inequality with double obstacle.

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Acknowledgements

I am grateful to the reviewers for bringing [1, 8] to my attention.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, 60660, USA

    E. N. Barron

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  1. E. N. Barron
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Correspondence to E. N. Barron.

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The work was supported in part by a Grant NSF-DMS 1515871.

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Barron, E.N. Reach-Avoid Differential Games with Targets and Obstacles Depending on Controls. Dyn Games Appl 8, 696–712 (2018). https://doi.org/10.1007/s13235-017-0235-5

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  • DOI: https://doi.org/10.1007/s13235-017-0235-5

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