Properties and approximate construction of the set of trajectories of the control system described by an affine integral equation

In this thesis the set of trajectories of the control system is investigated. It is assumed that the behavior of control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have integral constraints. The dependence of the set of trajectories on the various parameters of the system is studied and an approximation method is obtained for numerical calculation of the set of trajectories. The set of admissible control functions is replaced by the set which consists of a finite number of control functions. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated. It is proved that in the appropriate specifying of the discretization parameters, evaluated Hausdorff distance stands sufficiently small.