Abstract
We prove the existence of a lower semicontinuous value function for Bolza problem in differential games with state-constraints. As a byproduct, we obtain a new estimation of trajectories of a control system by trajectories with state constraints. This result which could be interesting by itself enables us to build a suitable strategy for constrained differential games. We also characterize the value function by means of viscosity solutions and give conditions under which the value function is locally Lipschitz continuous.
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Work supported by the European Community’s Human Potential Program under contract HPRN-CT-2002-00281, [Evolution Equations].
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Bettiol, P., Cardaliaguet, P. & Quincampoix, M. Zero-sum state constrained differential games: existence of value for Bolza problem. Int J Game Theory 34, 495–527 (2006). https://doi.org/10.1007/s00182-006-0030-9
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DOI: https://doi.org/10.1007/s00182-006-0030-9