Study On Game Control Of Networked Control Systems With Packet Dropouts

In recent years,with the popularization of networked information society,net-worked control systems(NCSs)play a more and more important role in daily life.NCSs have been widely used in unmanned aviation,automated highway system,signal processing and other fields because of the advantages of low consumption,high flexibility,easy installation and maintenance.Data packet transmission is one of the most important features that distinguishes NCSs from traditional control sys-tems.However,due to the limited bandwidth and the interference of hackers and malware during the transmission process,the data packets may be lost during the transmission process,which affect the performance of the NCSs,and even destroy the stability of the system.The packet dropouts problem of one controller and one performance index in the NCSs has been studied in depth.With the rapid develop-ment of drone technology and unmanned vehicle technology,it becomes meaningful to study the multi-controller and multi-objective optimization problems affected by packet dropouts in NCSs.In this paper,feedback strategies of Nash game and Stack-elberg game are studied for a class of NCSs with packet loss.The main contributions and innovations are as:On the one hand,we consider the feedback Nash equilibrium strategy for discrete time NCSs in finite horizon with packet dropouts.Firstly,using the maximum principle,the necessary and sufficien-t condition for the existence of solutions in feedback Nash equilibrium strategy is derived and the analytical solution of the two controllers is a linear feedback for-m of optimal estimation,and the optimal feedback gain matrices are calculated by decoupling the forward and backward stochastic difference equations(FBSDEs),where the separation principle holds in this case.Secondly,based on the dynamic programming method and the complete of square method,the sufficient condition for the existence of feedback Nash equilibrium strategy for discrete systems with packet loss in finite horizon is obtained,where the results is consistent with that of the maximum principle.That is,the expression of the controllers in feedback Nash equilibrium strategy based on the iterative calculation of the two coupled Riccati equations is a linear form of the optimal state estimation.On the other hand,we consider the feedback Stackelberg strategy for discrete time NCSs in finite horizon with packet dropouts.Based on the matrix maximum principle,the sufficient con-dition for the existence of feedback Stackelberg strategy with packet loss in finite horizon is obtained,and the analytical solution of the optimal controllers is a linear feedback form of state estimation.The key technique is to optimize the followers and the leaders successively.Firstly,we construct the Hamiltonian function of the follower.The corresponding Riccati equation and feedback gain matrix of the fol-lower are obtained by the matrix maximum principle.It is found that the follower's feedback gain matrix is a function of the leader's feedback gain matrix.Secondly,we consider the optimization problem of the leader,which is transformed into an optimal control problem satisfying a forward constraint.Constructing the Hamilto-nian function of the leader,the Riccati equation and the feedback gain matrix of the leader are obtained by the matrix maximum principle.In this way,the analytical solution of the optimal feedback Stackelberg strategy is obtained by decoupling the two coupled Riccati equations.Separation principle holds in this case.The main contents are listed as follows in the order of chapters:In the first chapter,we introduce the topic selection background and the research status of Nash game problem and Stackelberg game problem.In the second chapter and the third chapter,the main problems of the feedback Nash equilibrium strategy and Stack-elberg strategy for discrete time NCSs with packet dropouts in finite horizon are described and the relevant conclusions are derived,respectively.And at the end of each chapter,the validity of the results is verified by numerical simulation.In the last chapter,we summarize the whole paper and look forward to the future work.