Theory of minimum time discrete regulators

Abstract

This paper unifies and extends the ideas and techniques used by the authors in relation with the minimal time regulator problem. The system considered is a multiple input system described by a differential equation of the form $ = F(x) + Bu(t) where u is either a PAM or PWM bounded control vector. This paper consists of five sections. In the first, the problem is carefully stated in a suitable general setting, and the concept of optimal strategy is defined; in the second, an optimal strategy for a multiple input PAM system with a completely controllable linear plant is described fully, and a special case is discussed; in the third, the concept of equivalent optimal strategies is defined, and sufficient conditions for equivalence are indicated. In the fourth section equivalence is used to derive the optimal strategy of a PWM system whose linear plant has real and distinct eigenvalues, and finally in the last section, some extensions are mentioned.