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In this paper we study the problem of finding the optimal feedback control that can keep an agent within an interval for at least a certain amount of expected time with the least energy. The dynamics of the agent are subject to the perturbation of random noises, and thus are given by a stochastic differential equation. By formulating the problem as an optimal control problem, we propose a solution by using the maximum principle and finding a first integral to the resulting differential equations. Some numerical simulations are presented to illustrate the results.