Conflict controlled processes with discontinuous trajectories

Game approach problems for dynamic processes with impulse controls

“…In each case, we have obtained sufficient solvability conditions for the approach problem in a finite time. The paper continues the studies started in [19] and employs the results from [9].…”

“…As follows from [4,5], the solution of system (19) for the selected controls of the players exists for any initial condition z z ( ) 0 0 = , is unique, and is an absolutely continuous function on the intervals ( ,…”

“…Let T T z 0 1 0 0 Î ( , ) g , where z 0 is the initial state of process (19) and g 0 is the fixed set of selectors (20). …”

“…To illustrate the results presented above, let us use an example (from [19]) of a game problem with simple motions and impulse controls.…”

“…THEOREM 3. If Condition 5 is satisfied for the process(19) with the terminal set (2) and an impulse control of the evader, and the set M is convex; the set T z is nonempty for the initial state z 0 and the set of selectors g 0 , then it is possible to bring the trajectory of process(19) from the initial state z 0 to the terminal set M * at the instant T 0 for any…”