On the Equivalence of Discrete Systems in Time-Optimal Control

Abstract

It is shown in this paper that under a transformation which maps the state space of a system onto a sequence space in a one-to-one manner, time-optimal discrete regulator systems with different dynamics and modulators can be brought to equivalence and that this fact may be used to construct an optimal control strategy for one system from the known optimal control strategy of another one. In particular, the optimal control strategy for a pulse-width-modulated discrete system with a plant described by an nth order linear differential equation is derived in this manner.