Abstract:
A positional differential game of the approach-evasion of a conflict-controlled motion and a goal set within a given set is considered. Use is made of a solution of the associated boundary-value problem for a parabolic equation degenerating as the diffusion term vanishes to a Hamilton–Jacobi type equation, which is typical for techniques in the theory of differential games. Based on this, a control scheme with a stochastic guide is developed.
Keywords:approach-evasion alternative, strategy, probabilistic process, Ito equation, Lyapunov function.