Optimal Control And Stabilization Of Systems Over Multiple Parallel Fading Channels And Transmission Delays

With the progress of communication technology and the development of network technology,networked control system is widely used in many fields.However,the networked control system will also be affected by the network transmission environment,resulting in many uncertainties in the system.Due to the bandwidth limitations and the external noise interference during the data transmission,network-induced uncertainties such as data packet loss and transmission delay will occur.In addition,due to industrial development and technological innovation,the control system is becoming more and more complex.In a multi-parallel channel system,the channel fading will occur.Controller design for systems where these uncertainties coexist also becomes more complex.Therefore,the optimal control and stabilization of systems with multiple parallel fading channels and transmission time delays is of great significance and challenging at the same time.In this paper,the optimal control and stabilization problems of networked control systems with multiple parallel fading channels and transmission time delays are studied.Four types of systems are considered,such as the Markov jump linear systems with multi-parallel multiplicative noises,the networked control systems with multi-parallel Markov fading channels,the systems with transmission delays,and deterministic two-dimensional discrete control systems.Based on the stochastic maximum principle,the Lyapunov function approach,the Riccati equation,and the two-dimensional deterministic maximum principle,the finitehorizon optimal controllers and stabilization conditions subject to different systems are developed.The main contents are as follows:The problem of indefinite optimal control and stabilization of Markov jump systems with multi-parallel multiplicative noises is studied.In this situation,the state and control weight matrices of the system are allowed to be indefinite.A random diagonal matrix is used to describe the multiplicative noise with different fading characteristics in different transmission channels.By solving the forward and backward stochastic difference equations,an optimal controller in finite horizon is given.Based on the algebraic Riccati equations,the stabilizability condition of the stochastic Markov jump system with indefinite matrix in the performance index is proposed.The optimal control and stabilization problems of stochastic systems with multiple parallel Markov fading channels are studied.For such systems,by introducing a new multi-modal Markov chain,the problem is transformed into the optimal control and stabilization problem of general Markov jump systems.Furthermore,a new maximum principle suitable for the diagonal form Markov packet loss is proposed,and a set of coupled difference Riccati equations are established in the finite horizon,and the explicit solution of the optimal controller is obtained.According to the optimal performance index in finite horizon,a modified Lyapunov function is defined,combined with a set of coupled algebraic Riccati equations,the necessary and sufficient conditions for the mean square stability of the system and the optimal controller in infinite horizon are given.The optimal control and stabilization problems of systems with multi-parallel fading channels and transmission time delays are studied.Similar to the previous problem,by introducing a new multimodal Markov chain,this problem is firstly transformed into the optimal control and stabilization problem of a general Markov jump linear system with input time-delay.Based on the converted system,a new maxima principle suitable for diagonal form Markov packet loss with time delay is proposed.Using the coupled difference Riccati equations,the conditions for the optimal controller to be solved are given,and the analytical solution of the finite horizon optimal controller is deduced.By analyzing the convergence of the coupled difference Riccati equations in the finite horizon,the optimal controller and stability conditions in the infinite horizon are obtained.The optimal control problem of deterministic two-dimensional discrete control systems is studied.Based on the Givone-Roesser model,the Lagrangian multipliers are first introduced to construct the Hamiltonian equation,and then the maximum value principle of the twodimensional discrete network control system is given.On this basis,using the obtained twodimensional difference Riccati equation,the design of the optimal controller for the deterministic two-dimensional discrete network control system is completed.