Optimal Control of a Stochastic System: State-Costate Analysis

E. Khmelnitsky and G. Singer (Israel)


Stochastic control, Diffusion process, Threshold policy


We consider infinite and finite time horizon, discounted cost minimization problems for a system perturbed by a Wiener process. The controller is bounded in magnitude and allowed to control the drift parameter of the process. Using the necessary conditions of optimality, which are expressed in terms of costate dynamics, we prove the optimality of a threshold control policy. The threshold line is calculated either analytically for an infinite time horizon, or numerically for a finite time horizon. The policy is global in the sense that controls for all initial conditions in a region of the state space are obtained.

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