Research On LQ Control And Game Theory Of Networked Systems With Asymmetric Informatio

Most existing works mainly focus on the study of the control problems for the networked systems with the same information structure,in which the networked systems contain either only one controller or multiple controllers with the same information.For this situation,the LQ control and Stackelberg game problems have been well solved.While,in practice,the networked systems contain multiple controllers/decision variables,and each controller/decision variable may access different information sets,which is called the networked systems with the different information structure.The information asymmetry property can cause the coupling of the controllers/decision variables,making it difficult to find the optimal strategy.However,there are few research results on the LQ control and game problems for the networked systems with the different information structure,and some basic problems have not been solved.Therefore,the study of the LQ control and game problems for the networked systems with the different information structure has important theoretical significance and potential application value.This thesis focuses on the study of the LQ control problem and Stackelberg game problem for the networked systems with the different information structure,and the optimal control strategies are given by using the maximum principle,orthogonal decomposition and Lyapunov stability analysis.The main contributions and research contents are as follows:Firstly,for the networked systems with the different information structure,the LQ optimal control and stabilization problems are investigated for the networked systems with different transmission delays and packet dropouts.The considered system contains multiple sensors,multiple controllers and multiple actuators.In view of the different transmission delays and packet dropouts,each controller may access different information sets.The maximum principle of the asymmetric information networked systems is derived by using the convex variational principle,and the necessary and sufficient conditions for the LQ optimal control problem are developed.Based on the orthogonal decomposition approach,the obstacles caused by the coupling of the multiple controllers and the packet dropouts are overcome,and the finite horizon optimal state feedback controllers are obtained.In addition,for the infinite horizon stabilization problem,a sufficient stabilization condition for the systems is obtained by constructing a new Lyapunov function.It is proved that if the given algebraic Riccati equation admits a unique positive definite solution,the asymmetric information networked system is mean square stabilizable.Secondly,the Stackelberg game problem of the networked systems with the different information structure is also studied.Due to the different status of the decision variables(two players)in the systems,the information structure of the decision variables is asymmetric.Based on the maximum principle,it is proved that the optimal strategy of the Stackelberg game problem depends on the solution of a set of the forward and backward stochastic difference equations,and the sufficient and necessary conditions for the Stackelberg game problem are also given.Finally,a feasible solution to the Stackelberg game problem for the networked systems with the different information structure is obtained under the assumption of the linear relationship between the costates.