Quasilinear conflict-controlled processes with additional restrictions

A class of conflict-controlled processes 1–3] with additional (“phase” type) restrictions on the state of the evader is considered. A similar unrestricted problem was considered in 4]. Unlike 5, 6] the boundary of the “phase” restrictions is not a “death line” for the evader. Sufficient conditions for the solvability of the pursuit and evasion problems are obtained, which complement a range of well-known results 5–10].^‡