Additive Control of Stochastic Linear Systems with Finite Horizon

摘要

This reprint considers a dynamic system whose state is governed by a linear stochastic differential equation with time-dependent coefficients. The control acts additively on the state of the system. The objective is to minimize and integral cost which depends upon the evolution of the state and the total variation of the control process. It is proved that the optimal cost is the unique solution of and appropriate free boundary problem in a space-time domain. By using some decomposition arguments, the problems of a two-sided control, i.e. optimal corrections, and the case with constraints on the resources, i.e. finite fuel, can be reduced to a simpler case of only one-sided control, .e. a monotone follower. These results are applied to solving some examples by the so-called method of similarity solutions.