Mathematical aspects of the synthesis of linear minimum response-time controllers

A procedure is presented for finding, in a systematic matter, the forcing function to be applied to a process to give time-optimal control. The results are limited to the case where the process to be controlled has dynamics which are completely known and are adequately described by a system of linear differential equations. It has also been assumed that the process is not subject to unknown disturbances. The implication of the method presented is that any process as limited above can be time-optimally controlled, in those cases where a time-optimal controller exists, provided an underlying system of transcendental equations can be solved. This system of transcendental equations can be quite easily solved for systems of order less than three, even with two forcing functions, and for various other special cases of higher order. The results of a study which indicate that the method can be applied in quite general situations are being presented elsewhere