Singularities of Attainability Domains with a Pulse-Limited Control Action

Abstract

Linear stationary systems with single-control (perturbing) action are considered. The impulse of control actions is considered limited. Some properties of the boundaries of attainability domains are studied. It is shown that the boundary of the attainability domain can have flat regions, regions of ruled surfaces, edges, and conical angular points. An attainability domain is not strictly convex if there are straight edges and/or flat regions on the boundary. The behavior of the boundaries of the attainability domains with increasing time is studied. A third-order system with a threefold zero eigenvalue (triple integrator) is considered as an example. The structure of the attainability domain of this system is analytically investigated in three-dimensional space. An attainability domain is constructed numerically for some time values.