Time Optimal Control of a Linear Diffusion Process

Abstract

The applicability of the Laplace transformation for the determination of the time optimal control of a linear diffusion process with amplitude constraints on the control is presented. The method—which can be interpreted as requiring a control whose transform in combination with the initial condition places zeroes at the poles of the open loop transfer function—is used to derive the optimal control function on the assumption that it is bang-bang, i.e., it is always at its limiting values. It is shown that the transfer of the system from a given initial state to a desired final state can be accomplished in finite time. A physical interpretation of the numerical results obtained is given., based on a transmission line analogue, and the actual time response for suboptimal controls is used to confirm theoretical estimates.