Study On Linear Two Times Optimal Control Of Constrained Mean Field

With the development of science and technology,control systems are becoming more and more complex and often are constrained by various conditions,so optimal control becomes the research of modem control theory,which plays a more and more important role in people's daily Iife.The optimal control problem is to seek the optimization method of control system under certain constraint conditions and make the performance index reach the maximum or minimum of the system which satisfies the conditions.In this thesis,the optimal control problem of the mean field discrete time/continuous time systems with constraints is studied.The necessary condition for the existence of the optimal state feedback solution is proved by the Lagrange multiplier theorem and the minimum principle.The specific research work as follows:1.We study the stochastic linear quadratic optimal control problem of the mean field discrete time system under constrained condition.First,the mean field discrete time system is given,and the objective function of the admissible control set is determined.Then,the Frechet differential derivative of each target function is calculated and the optimal state feedback solution is obtained.The necessary condition of the existence of the optimal state feedback solution is proved by using the Lagrange multiplier theorem and the minimum principle.Finally,a numerical example is used to verify the correctness of the conclusion.2.We study the stochastic linear quadratic optimal control problem of the continuous time mean field system with a constrained.First,a mean field continuous time system is given,and the perforlance index of the optimal control and optimal control problen is determined.Then,by converting the original problem into a deterministic problem,the optimal state feedback is obtained.The necessary condition for the existence of the optimal state feedback solution is proved by the Lagrange mean value theorem and the minimum principle.Finally,the correctness of the conclusion is verified by a numerical example.