Properties of Attainability Sets for Dynamic Systems with Discontinuous Trajectories

Abstract

The attainability set for a dynamic system with impulsive integrally bounded control is shown to be compact and continuously dependent on the parameters and a control resource. Although such a set may consist of discontinuous trajectories, it turns out to be continuous as a multivalued mapping defined on [t ₀, ϑ]. The connectedness property for attainability sets is proven. Some methods to determine such sets are presented. For a particular class of bilinear systems, the number of control impulses needed for the system to pass to a given point of the attainability set is estimated. Similar problems for dynamic systems with absolutely continuous trajectories has been studied in [25, 14, 108].