Solution of the Time-optimal Problem in the Linear System with Delay

Abstract

In this paper the authors intend to give the general procedure to solve the time-optimal problem in the linear system with delay by applying the method of maximum principle. In the system with delay, the solution of the problem contains the essemtially different difficulties in contrast with the system without delay. The largest difficulty exists in that the auxiriary system involves the advanced arguments. This difficulty is removed by introducing the inverse-time system and applying the iteration procedure. The same inverse-time concept can be used for the mechanization of the computation procedure by an analog computer with a help of a simple circuitry. The concept of the isochrone is introduced in a certain limitted sense which gives clear understamding of the structure of the problem.