Quasilinear pursuit differential game with a simple dynamics under phase constraints (Q5951084)

On a fixed closed time interval the author considers a pursuit differential game with a convex compact target set under a phase constraint in the form of a convex closed set. He constructs a convex compact guaranteed capture set similar to an alternating Pontryagin sum and defines the guaranteed piecewise-programmed strategy of the pursuer ensuring the hitting of the target set by the phase constraint in finite time. Under certain conditions, it is proved the convergence of the constructrd alternating sum in the Hausdorff metric to a convex compact set, which is an analog of the alternating Pontryagin integral for the differential game.