Deterministic Equivalent for a Continuous Linear-Convex Stochastic Control Problem

摘要

The authors consider a finite horizon control model with additive input. There are two convex functions which describe the running and the terminal costs within the system. The cost of input is proportional to input and can take both positive and negative values. It is shown that there exists a deterministic control problem whose optimal cost is the same as the one in the stochastic control problem. The optimal policy in the stochastic problem consists of keeping the process as close to the optimal deterministic trajectory as possible.