Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with It&#xf4;&#x2019;s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially,  present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem.
['Li Chen', 'Zhen Wu', 'Zhiyong Yu']
I am writing a research paper on a idea Delayed Stochastic Linear-Quadratic Control Problem and Related Applications
[{"from": "human", "value": "I am writing a research paper on a idea Delayed Stochastic Linear-Quadratic Control Problem and Related Applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  discuss a quadratic criterion optimal control problem for stochastic linear system with delay in both state and control variables. This problem will lead to a kind of generalized forward-backward stochastic differential equations (FBSDEs) with It&#xf4;&#x2019;s stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations. Especially,  present the optimal feedback regulator for the time delay system via a new type of Riccati equations and also apply to a population optimal control problem."}]