Optimal Control And Stabilization For Networked Control System With Limited Channels

As a hot topic in the field of control,networked control systems have been widely applied in many industrial fields with the innovation and development of network technology and control theory.However,due to the introduction of network channels,the physical limitations can negatively affect the control performance of networked control systems,resulting in phenomena such as data packet loss,network delays,and channel fading caused by bandwidth limitations,network congestion,external interference signals,and other factors.On the other hand,various communication protocols used in network communication processes also have a significant impact on the performance and stability of control systems.Therefore,by designing appropriate optimal control strategies,the system performance can be maximized,and system stability can be ensured.This is of great significance for improving the control efficiency and accuracy of modern industrial automation systems.This article systematically investigates the optimal control and stabilization problems of networked control systems with limited channels.Specifically,it focuses on three situations:optimal control and stabilization of asymmetric information systems caused by packet loss channels,control and stabilization of networked Markov jump linear systems with multiple parallel erasure channels,and control based on communication protocol scheduling.Methods and tools such as the stochastic maximum principle,Riccati equation,and forward-backward stochastic difference equation are applied to design state feedback control and output feedback control algorithms.The main contributions are as follows:The optimal control and stabilization of the asymmetric information systems with packet loss channels are studied.Both networked systems with memoryless loss channels and networked Markov jump systems with multiple parallel erasure channels are investigated.The corresponding stochastic maximum principles are proposed,and the forward-backward stochastic difference equations are given.The finite horizon optimal control and infinite horizon stabilization problems of these discrete-time systems are solved by coupled difference Riccati equations and algebraic Riccati equations.The optimal control and stabilization of networked control systems with multiple Markovian packet loss channels are studied.Two types of systems are considered: systems with this type of channel only between the controller and the actuator and systems where this type of channel coexists on both the channels between the controller and the actuator and the channels between the sensor and the controller.The corresponding state feedback control and output feedback control designs are completed.The model processing method for the systems with multiple parallel Markovian packet loss channels is proposed,and the system is converted into a Markov jump linear system for analysis.The design of state feedback control and stabilization is accomplished by solving the forward-backward Markovian difference equations.For the systems with coexisting channels,a set of Riccati equations are established to design the optimal filter to obtain the optimal estimation of the system state.After the verification of the separation principle,the solution to the optimal output feedback control is given.The optimal control problems of networked control systems based on communication protocols are studied.Quadratic optimal controllers are designed for systems subject to Round-Robin protocol and stochastic communication protocol.In light of model conversion and Markov chain reconstruction,these systems are transformed into Markov jump linear systems,and the corresponding stochastic maximum principle and forward-backward stochastic difference equations are established.Based on the coupling difference Riccati equations,the sufficient and necessary conditions for the existence of the solution to the optimal control problem in these two situations are obtained,and the analytical expression of the optimal controllers are derived.