Study On LQ Control Of Mean Field Stochastic Systems With Asymmetric Information Controller

The linear quadratic(LQ)control problem of mean field stochastic systems is a combination of mean field theory and modern control theory,and its system equations are usually described by the mean field stochastic difference/differential equations.The LQ control problem of mean field stochastic systems is not only an important part of modern control theory,but also a wide range of applications in large populations stochastic dynamic games and various physical and sociological dynamical system problems.It is worth noting that the LQ control problem for mean field stochastic systems with a single controller has been well studied,but there are still many basic theoretical problems for the LQ control problem of the mean field stochastic systems with multiple asymmetric information controllers.In this thesis,we will study the LQ control problem of discrete time and continuous time mean field stochastic systems with multiple asymmetric information controllers.The main contents,results and innovations are listed as follows in the order of chapters:1.LQ control problem for discrete time mean field systems with multiple controllers with different time delay information.Firstly,the maximum principle of discrete time mean field stochastic LQ control problem with multiple delay information controllers is proved by convex variational method,and a set of mean field forward and backward stochastic difference equations are obtained.Then,the orthogonal decomposition method is proposed to deal with the asymmetric information pattern effectively.Next,the relationship between the control state and the co-state is obtained by decoupling the mean field forward and backward stochastic difference equations,and then the optimal control strategy based on a set of asymmetric Riccati equations is designed.In addition,a simulation example is given to verify the validity of the results.It should be emphasized that the results obtained solve the LQ optimal control problem of discrete time mean field stochastic systems,and provide some theoretical reference for improving the mean field theory in the future.2.LQ control problem for continuous time mean field systems with asymmetric information controllers.The maximum principle of LQ control for continuous time mean field systems with asymmetric information controllers is derived by variational method.Based on a theoretical method for solving forward and backward stochastic differential equations,the nonhomogeneous linear relationship between stochastic control state and co-state is established.The explicit expression of optimal control strategy is obtained by combining the solution expression of stochastic differential equations and the method of decoupling mean field forward and backward stochastic differential equations.Finally,a simulation example is given to verify the effectiveness of the designed optimal control strategy.The main innovations are as: For the LQ control problem of continuous time mean field systems with asymmetric information controllers,the obstacle of system adaptability destruction caused by the appearance of mean field terms and the trouble caused by asymmetric information are overcome.Secondly,the resolvable conditions and optimal control strategy for LQ control problems of continuous time mean field stochastic systems with asymmetric information controllers are derived.