COMPUTING THE REACHABLE SET BOUNDARY FOR AN ABSTRACT CONTROL SYSTEM: REVISITED

Abstract

A control system can be treated as a mapping that maps a control to a trajectory (output) of the system. From this point of view, the reachable set, which consists of the ends of all trajectories at a given time, can be considered an image of the set of admissible controls into the state space under a nonlinear mapping. The paper discusses some properties of such abstract reachable sets. The principal attention is paid to the description of the set boundary.

Keywords

• reachable set, nonlinear mapping, control system, extremal problem, maximum principle