On the properties of the set ofp-integrable trajectories of the control system with limited control resources

摘要

The properties of the set of trajectories of the control system described by Urysohn type integral equation are considered. It is assumed that the system is affine with respect to the control vector and control functions are chosen from the bounded and closed ball of the spaceLq(E;Rm),q>1. The trajectory of the system is the function from the spaceLp(E;Rn),1/q+1/p=1, which satisfies the system's equation almost everywhere. The path-connectedness and compactness of the set of trajectories are proved. The existence of the optimal trajectories in the optimal control problem with lower semicontinuous payoff functional is discussed.