Time Optimal Control of a Linear Diffusion Process

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.