Article ID Journal Published Year Pages File Type
6952516 Journal of the Franklin Institute 2018 15 Pages PDF
Abstract
In this work, we consider an optimal control problem of a class of stochastic differential equations driven by additive noise with aftereffect appearing in control. We develop a semigroup theory of the driving deterministic neutral system and identify explicitly the adjoint operator of the corresponding infinitesimal generator. We formulate the time delay equation under consideration into an infinite dimensional stochastic control system without time lag by means of the adjoint theory established. Consequently, we can deal with the associated optimal control problem through the study of a Hamilton-Jacob-Bellman (HJB) equation. Last, we present an example whose optimal control can be explicitly determined to illustrate our theory.
Related Topics
Physical Sciences and Engineering Computer Science Signal Processing
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