ON THE EXISTENCE OF epsilon-OPTIMAL TRAJECTORIES OF THE CONTROL SYSTEMS WITH CONSTRAINED CONTROL RESOURCES

Abstract

The control system described by a Urysohn type integral equation is considered. It is assumed that the admissible control functions are chosen from the closed ball of the space L-p, p > 1, with radius r and centered at the origin. Precompactness of the set of trajectories of the control system in the space of continuous functions is shown. This allows to prove that optimal control problem with lower semicontinuous payoff functional has an epsilon-optimal trajectory for every epsilon > 0.