8th International Conference on Curves and Surfaces, Paris, France, 12 - 18 June 2014, vol.9213, pp.280-288
The set of trajectories of the control system with limited control resources is studied. It is assumed that the behavior of the system is described by a Volterra type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The closed ball of the space L-p (p > 1) with radius mu and centered at the origin, is chosen as the set of admissible control functions. It is proved that for each fixed p the set of trajectories is Lipschitz continuous with respect to mu and for each fixed mu is continuous with respect to p. The upper evaluation for the diameter of the set of trajectories is given.