Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays

Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays

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The purpose of this paper is to find the time-optimal TV control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators.Our research approach is to construct Underwear a fundamental solution for corresponding linear systems and establish variations of a constant formula of solutions for given stochastic equations.The existence result of time-optimal controls for one point target set governed by the given semilinear stochastic equation is also established.