Minimum-time control of linear multivariable systems

The theoretical basis necessary for the determination of minimum-time controllers has been known for some time; however, there have been few practical implementations of such controllers for multi-input systems owing to the numerical difficulties which arise in their evaluation. In this work, it is shown that these difficulties are caused by the corners which exist in the minimum-time isochrones of such systems. It is found that these corners are associated with changes in the number of switchings in the minimum-time controller. The results of this analysis are used to provide a means whereby these numerical difficulties, inherent in the evaluation of minimum time controllers, may be overcome, or in some cases avoided completely.