The properties of attainable sets of control systems with integral constraints on control functions

In this thesis, attainable sets of control systems with integral constraints on control functions are investigated. It is assumed that the behavior of control system is described by a differential equation which is nonlinear with respect to the phase state vector and control vector. It is shown that the attainable set is not closed, but the set of solutions is a precompact subset of the spaceof continuous functions. It is proved that the attainable sets of the system continuously depend on the initial conditions and other parameters of the system.The noncompact admissible control functions set is replaced by a compact admissible control functions set (integral and geometric constrained also Lipschitz continuous control functions where the Lipschitz constant of control functions are restricted by the same constant) and the Hausdorff distance between the attainable sets generated by these admissible control functions setsis evaluated. The dependence of this distance on the constants specifying the geometric constraint and the constraint on the Lipschitz constant is studied. It is proved that, if these constants are sufficiently great then the Hausdorff distance between these attainable sets is sufficiently small.