Random Delayed Optimal Control Problem With Restriction
Differential equations with delay play an important role in many fields of the physical sciences, technology, engineering, economy, and so on, whenever memory effects must be taken into account.
In other hand, there are many phenomena such as the evolution of the stock price, the pricing of options for securities markets, portfolio-consumption choice and other dynamical systems are exposed to random influences which cannot be ignored.Therefore there is an increasing need to extend the deterministic models by including random influences or noise. Different sources of affects will require different modeling of the noise and the lag.
Recently, a lot of applications in engineering, mechanics, biology, life science, finance and other fields, the optimization problems of stochastic systems with delay have attracted increasing interset.
This investigation deals with optimal control problems for random delayed systems.
Necessary condition of optimality for abovementioned dynamical systems with endpoint constraint is obtained.