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Numerical Construction of Viable Sets for Autonomous Conflict Control Systems

Center for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching 85747, Germany
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Mathematics 2014, 2(2), 68-82; https://doi.org/10.3390/math2020068
Received: 29 December 2013 / Revised: 6 March 2014 / Accepted: 2 April 2014 / Published: 11 April 2014
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
A conflict control system with state constraints is under consideration. A method for finding viability kernels (the largest subsets of state constraints where the system can be confined) is proposed. The method is related to differential games theory essentially developed by N. N. Krasovskii and A. I. Subbotin. The viability kernel is constructed as the limit of sets generated by a Pontryagin-like backward procedure. This method is implemented in the framework of a level set technique based on the computation of limiting viscosity solutions of an appropriate Hamilton–Jacobi equation. To fulfill this, the authors adapt their numerical methods formerly developed for solving time-dependent Hamilton–Jacobi equations arising from problems with state constraints. Examples of computing viability sets are given. View Full-Text
Keywords: differential game; state constraint; viability kernel; backward procedure; value function; Hamilton–Jacobi equation differential game; state constraint; viability kernel; backward procedure; value function; Hamilton–Jacobi equation
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Botkin, N.; Turova, V. Numerical Construction of Viable Sets for Autonomous Conflict Control Systems. Mathematics 2014, 2, 68-82.

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