A fast time-optimal control synthesis algorithm for a class of linear systems

The paper deals with a new approach for synthesis of time-optimal control for a class of linear systems. It is based on the decomposition of the time-optimal control problem into a class of decreasing order problems, and the properties and relations between problems within this class. First, the problems´ state-space properties are analyzed, and then the optimal control is obtained by using a multi-step procedure avoiding the switching hyper surface description. The emphasis in this paper is on the optimal control synthesis stage of the approach proposed. A property of the considered class of problems is studied which enables development of a fast algorithm for synthesis of time-optimal control without using the switching hyper surface.