Stability And Control Of Stochastic Networked Systems With Lipschitz Nonlinearities

Networked control systems (NCSs) have been studied intensively in theautomatic control field in the past a few years. NCSs are spatially distributedsystems in which the communication between sensors, actuators, and con-trollers occurs through a shared bandlimited digital communication network.Such NCSs make it possible to share process data and marketing informationplant-widely, which improves availability, operating safety, reliability and en-vironment protection of the production. In the control of NCSs, there aremany new problems such as the intermittent data packet losses, the network-induced time delay, and communication constrains. The intermittent datapacket losses and the network-induced time delay are known to be two ofthe main causes for the performance deterioration or even the instability ofthe controlled networked system. It is well-known that there commonly existthe nonlinearities in practical control systems, and most of the nonlineari-ties satisfy the Lipschitz condition, for example, the trigonometric functionnonlinearities in the robot and the Aircraft Systems. Lipschitz nonlinearsystems is a kind of nonlinear systems system which the nonlinear compo-nents of the state and input relative to the system state variables satisfythe Lipschitz condition. So the research about networked nonlinear systemswith Lipschitz is very important both in theories and applications, and also avery representative and challenging problem. We thoroughly investigate thestability-analysis and controller-synthesis problems of networked nonlinearsystems with global Lipschitz nonlinearities with random packet dropout orrandom network-induced time delay. The main contents are as follows:Firstly, this paper introduce the origin,development,specialty and thecurrent research status of NCSs roundly and detailedly, and analyze theseveral base problem,typical research approaches, and at the same time we advance our opinion about the research of NCSs. The contributions of theworks are listed in the following.1. The observer-based H_∞control problem of networked nonlinearsystems with global Lipschitz nonlinearities and with the random packetlosses in both the sensor-to-controller and sensor-to-controller communica-tion channels is investigated. The random packet loss is modelled as aBernoulli distributed white sequence with a known conditional probabilitydistribution. In the presence of random packet losses, based on the Lyapunovstability theory, su?cient conditions for the existence of an observer-basedfeedback controller are derived, such that the closed-loop networked nonlin-ear system is exponentially stable in the sense of mean square and a pre-scribed H_∞disturbance-rejection-attenuation performance is also achieved.And then an linear matrix inequality (LMI) approach for designing such anobserver-based H_∞controller is presented by solving a certain convex opti-mization problem. Finally, a simulation example is used to demonstrate thee?ectiveness of the proposed method.2. The observer-based H_∞control problem of networked nonlinear sys-tems with global Lipschitz nonlinearities and with the random communica-tion delays in both the sensor-to-controller and sensor-to-controller commu-nication channels is explored. The random communication delays is mod-elled as a Bernoulli distributed white sequence with a known conditionalprobability distribution. In the presence of communication delays, based onthe Lyapunov stability theory, su?cient conditions for the existence of anobserver-based feedback controller are derived, such that the closed-loop net-worked nonlinear system is exponentially stable in the sense of mean squareand a prescribed H_∞disturbance-rejection-attenuation performance is alsoguaranteed. And then an linear matrix inequality (LMI) approach for de-signing such observer-based H_∞controller is presented. With the help ofthe LMI solvers, the observer-based H_∞controller can easily be obtained bysolving a certain convex optimization problem. Finally, a simulation example is used to demonstrate the effectiveness of the proposed method.3. The observer-based H_∞control problem of networked nonlinear sys-tems with global Lipschitz nonlinearities and with multiple sensors with dif-ferent packet losses probabilities is studied. It is supposed that in the commu-nication channels from the multiple sensors to the controller each sensor hasan individual random data missing probability. The random packet loss ismodelled as a Bernoulli distributed white sequence with a known conditionalprobability distribution. In the presence of random multiple packet losses,based on the Lyapunov stability theory, su?cient conditions for the existenceof an observer-based feedback controller are derived, such that the closed-loop networked nonlinear system is exponentially stable in the sense of meansquare and a prescribed H_∞disturbance-rejection-attenuation performanceis also guaranteed. And then an linear matrix inequality (LMI) approach fordesigning such observer-based H_∞controller is presented. With the help ofthe LMI solvers, the observer-based H_∞controller can easily be obtained bysolving a certain convex optimization problem. Finally, a simulation exampleis used to demonstrate the e?ectiveness of the proposed method.4. The observer-based H_∞control problem of networked nonlinear sys-tems with global Lipschitz nonlinearities and with random multiple com-munication delays is investigated. Because of the limited bandwidth of thechannels, such random communication delays could occur, simultaneously, inthe communication channels from the multiple sensors to the controller andfrom the controller to the actuator. It is supposed that in the communica-tion channels from the multiple sensors to the controller each sensor has anindividual random delay probability. The random communication delay ismodelled as a Bernoulli distributed white sequence with a known conditionalprobability distribution. In the presence of random multiple communicationdelays, based on the Lyapunov stability theory, su?cient conditions for theexistence of an observer-based feedback controller are derived, such that theclosed-loop networked nonlinear system is exponentially stable in the sense of mean square and a prescribed H_∞disturbance-rejection-attenuation perfor-mance is also achieved. And then a linear matrix inequality (LMI) approachfor designing such an observer-based H_∞controller is presented. With thehelp of the LMI solvers, the observer-based H_∞controller can easily be ob-tained by solving a certain convex optimization problem. Finally, a numericalexample is used to demonstrate the e?ectiveness of the proposed method.