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

Yong Han Kang and Jin-Mun Jeong
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Yong Han Kang: Institute of Liberal Education, Catholic University of Daegu, Gyeongsan 38430, Korea
Jin-Mun Jeong: Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea

Mathematics, 2021, vol. 9, issue 16, 1-12

Abstract: The purpose of this paper is to find the time-optimal 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 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.

Keywords: stochastic differential equation; retarded control system; time-optimal control; admissible set; analytic semigroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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