8th International Conference on Curves and Surfaces, 2014, Paris, France, 12 - 18 June 2014, vol.9213, pp.280-288
© Springer International Publishing Switzerland 2015.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 Lp (p > 1) with radius μ 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 μ and for each fixed μ is continuous with respect to p. The upper evaluation for the diameter of the set of trajectories is given.