On the compactness of the set of L-2 trajectories of the control system

Abstract

In this paper, the compactness of the set of L2 trajectories of the control system described by the Urysohn-type integral equation is studied. The control functions are chosen from the closed ball of the space L2 with radius r and centered at the origin. Existence of an optimal trajectory of the optimal control problem with lower semicontinuous payoff functional is discussed.

Keywords

• control system
• Urysohn integral equation
• integral constraint
• compactness
• set of L-2 trajectories