A stochastic two-target pursuit-evasion differential game with three players moving in a plane
The differential game considered in the paper involves three players P, \(Q_ 1\) and \(Q_ 2\), and is based on a noise-corrupted kinematic model. Minimum turning radii of the players are: \(R_ P\), \(R_{Q_ 1}\) and \(R_{Q_ 2}\), respectively. It is assumed, however, that \(R_{Q_ 1}=R_{Q_ 2}=0\). The player P has a weapon system of range \(\rho_ P\) and a half-squint-angle \(\alpha\). The players \(Q_ 1\), \(Q_ 2\) have weapon systems with an all-aspect range \(\rho_ Q\). If the distance between P and \(Q_ i\) is not less than some fixed constant \(R_ 0\) then P and \(Q_ i\) will break off contact. The goal of P is to intercept at least one of \(Q_ 1\) or \(Q_ 2\), or to break off contact with at least one of them before being intercepted by either of them. The goal of \(Q_ 1\) and \(Q_ 2\) is that at least one of them will intercept P before P intercepts or breaks off contact with either of them. A simplified version of this game is considered at the end of the paper. Sufficient conditions on optimal strategies requiring the existence of some smooth solution to a nonlinear partial differential equation on a generalized torus in \({\mathbb{R}}^ 4\) are obtained.
two-targed stochastic differential pursuit-evasion games
scientific article; zbMATH DE number 4018821
scientific article