A closed-loop, approximately time-optimal control method for linear systems

In this paper, a method is developed for the closed-loop, approximately time-optimal control of a class of linear systems with a total effort constraint. This method is based on a special class of solutions of the Hamilton-Jacobi equation, called eigenvector scalar products. The procedure to be followed is systematically presented, and the method is shown to represent an effective compromise between system complexity and speed of response. In designing a closed-loop system using this method, the controller-computer must only solve algebraic equations, and hence the control can be computed continuously.This is to be contrasted with many of the present methods which require on-line solution of two-point boundary value problems, and hence discrete control. The method is illustrated by an example.