Observer-based Sliding Mode Control For Discrete Nonlinear Networked Systems

The networked control systems have attracted significant attention due to the rapid developments of network techniques.The networked control systems have been applied in many practical engineering systems such as spacecraft,vehicle suspensions,and manufacturing plants due primarily to its outstanding advantages,including resource sharing,low cost and high reliability.In networked control systems,network congestion will occur when information is transmitted between nodes with limited bandwidth on account of the introduction of the network as a communication medium.Subsequently,some inevitable phenomena will occur,such as transmission time delays,packet losses,etc.Therefore,it is of great practical significance to study how to reduce the influences of the network-induced phenomena in performance of system,and to develop suitable control scheme to make the system stability.In this paper,the robust sliding mode control problems for several kinds of discrete-time nonlinear networked systems have been investigated via observer-based strategy.The specific work is summarized as follows.Firstly,the problem of robust sliding mode control for a class of uncertain delayed systems with packet losses is investigated.The phenomena of packet losses are built mathematical model,the corresponding sliding surface and observer are designed based on the packet losses probabilities information.Subsequently,the event-triggered mechanism is introduced by making certain criteria to determine the data transmission based on the estimated states.Afterwards,sufficient criteria are derived to guarantee that the augmented system is stochastically stable by employing linear matrix inequality method and Lyapunov-Krasovskii functional.In addition,the observer-based sliding mode controller is constructed to ensure the reachability of sliding surface in the discrete case.Finally,the validity of proposed SMC approach is testified by providing an illustrative example.Secondly,the H_?sliding mode control problem is studied for networked systems with channel fading and randomly varying nonlinearities under uncertain occurrence probabilities.Here,the phenomenon of randomly varying nonlinearities is characterized by adopting Bernoulli distribution random variables,where some variables satisfy in the interval[0,1].The discrete sliding surface is designed with the help of the current estimated states.According the corresponding augmented system can be obtained.By employing Lyapunov-Krasovskii functional,inequality method and stability theory,sufficient criteria are derived to ensure that the augmented system is satisfied asymptotically stable in mean-square sense.Subsequently,the robust sliding mode controller is designed to ensure the reachability of sliding surface.Finally,the validity of proposed SMC approach is testified by providing an illustrative example.Thirdly,the finite-time H_?sliding mode control problem is investigated for a class of discrete-time system with channel fading based on non-fragile observer method.The Rice fading model is built to better reflect the phenomenon of channel fading where fading coefficients are Bernoulli distributed and mutually independent random variables.The sliding mode controller based on non-fragile observer is constructed by employing the information of channel coefficients.By adopting Lyapunov-Krasovskii functional,inequality approach and the auxiliary function,sufficient criteria are derived that the augmented system is stochastic finite-time stable(SFTS)and satisfies H_?performance.In addition,the sliding mode controller is constructed to ensure the reachability of sliding surface in the discrete case.Finally,the validity of proposed SMC approach is testified by providing an illustrative example.Fourthly,the finite time H_?sliding mode control problem is discussed for a class of uncertain time-delay systems with randomly occurring cyber attacks.The phenomena of randomly occurring cyber attacks are modeled via the Bernoulli distributed random variables.The corresponding observer and sliding mode surface are constructed by using the received signals from the sensor to the observer at the current moment.The proper Lyapunov-Krasovskii functional and linear matrix inequality method are selected to derive sufficient conditions that can ensure the stochastic finite-time stability and H_?performance of the augmented system.The expression forms of the gain matrices of the observer and controller can be derived by employing auxiliary function.Subsequently,the novel robust sliding mode controller is constructed that can force the system state trajectories onto a pre-specified sliding mode region.Finally,the validity of proposed SMC approach is testified by providing an illustrative example.