Convergence of Numerical Method for Time-Optimal Differential Games with Lifeline

Nataly V Munts,Sergey S Kumkov

doi:10.1007/978-3-030-56534-3_5

Convergence of Numerical Method for Time-Optimal Differential Games with Lifeline

Nataly V Munts, Sergey S Kumkov

https://doi.org/10.1007/978-3-030-56534-3_5

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Publication Date: Jan 1, 2020

Affiliation: N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences

#Player Wins #Hamilton–Jacobi Equation + Show 8 more

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Abstract

AbstractThis paper discusses time-optimal differential games with lifeline. In such games, together with a target set, whereto the first player tries to guide the system, another set is chosen (namely, it is called lifeline), with reaching which the second player wins. A numerical method solving time-optimal games with lifeline is suggested. This method constructs the value function as a viscosity solution of the corresponding boundary value problem for a Hamilton–Jacobi equation (HJE). A convergence of the method is proved. Theorems on coincidence of the value functions of time-optimal problems with and without lifeline are justified.

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