Level Sets of Value Function and Singular Surfaces in Linear Differential Games

Abstract

The paper deals with an algorithm of construction of level sets in linear differential games with fixed terminal time and convex payoff function depending on two components of the phase vector. Into this algorithm, the block for detection of singular points on the border of level set is included. Singular points give singular lines on the border of level set. Singular surfaces in the game space are collected using singular lines as skeleton. Examples of numerically calculated level sets and singular surfaces are represented.