Research On Sliding Mode Control Of Discrete Markov Jump Systems

Markov jump networked systems have widespread applications in the fields of fi-nancial technology,weather forecasting,speech recognition,etc.,which has attracted the attention of more and more scholars.It is of great theoretical and practical significance to study the stability and boundedness of Markov jump networked systems under the condi-tions of stochastic communication delays,network data packet losses,deception attacks,etc.This paper mainly studies the problem of sliding mode control for Markov jump net-worked systems under network-induced phenomena.Also,the sliding mode fault-tolerant control problem under the actuator fault and the sliding mode bumpless transfer control problem are discussed.The specific contents are as follows.First,the Bernoulli distributed stochastic variables are used to characterize the phe-nomena of packet losses and time-delays.Based on this,the problems of sliding mode H___∞control and finite-time sliding mode control are investigated for discrete Markov jump networked systems under the occurrence of packet loss and then the sliding mode passive control problem is investigated in the case of multiple communication time delays.Giv-en the occurrence of packet loss of the system’s output signal and the characteristics of occurrence probability,an observer is constructed for the system to estimate measure-ment output and state information.Further,the schemes of sliding mode H___∞control and finite-time sliding mode control are given for discrete Markov jump networked systems respectively based on the observer and average dwell time method.Besides,subject to discrete Markov jump networked systems under multiple communication time-delays,the corresponding scheme is proposed to ensure the finite-time boundedness with a passive performance of the considered system via the Lyapunov method.Numerical examples verify the effectiveness of the above scheme.Second,for discrete Markov jump networked systems under deceptive attacks,a new stochastic deception attack model is proposed in order to better align with the actual s-cenarios of network attacks.Considering the difficulty of obtaining real-time mode from the system,an asynchronous sliding mode observer based on the hidden Markov model is established,which can avoid the requirement of real-time knowledge of the system’s mode.Further,an augmented system is formed by the estimation system and the error system,and a proper Lyapunov functional is constructed for the augmented system.By performing forward differential operations along the augmented system,criteria for the stochastic stability of the system under stochastic deception attacks are provided.In ad-dition,the study proposes a new reaching condition associated with deception attacks,where the system’s sampling period will change to adapt to specific circumstances once the system is subjected to deception attacks.Through comparative simulations,it is found that the proposed sliding mode control algorithm based on the aforementioned reaching condition exhibits good resistance against stochastic deception attacks.Then,the problem of sliding mode fault-tolerant control design is investigated for Markov jump delayed systems,where the actuator failure phenomenon is portrayed using the effective factor and the nonlinear function.This study aims to construct a new finite-time sliding mode fault-tolerant controller,ensuring that the closed-loop system is finite-time bounded in the entire operational stage.The focus is to introduce a partitioning strategy for the control system and combine it with sliding mode control techniques to handle actuator failure issues.From a practical point of view,we fully take into account the difficulty of achieving an ideal sliding mode in the design of discrete sliding mode control.The partitioning strategy is utilized to deal with the sliding mode fault-tolerant control problem.Then,the finite-time boundedness of the closed-loop system can be guaranteed in two operational stages.The feasibility of the sliding mode fault-tolerant control scheme based on a partitioning strategy is verified through simulation examples.Finally,the problem of bumpless transfer for discrete Markov jump uncertain sys-tems is considered.The existing method is extended first and a common integral-type sliding surface is designed.Sufficient criteria are derived in order to ensure the bump-less transfer performance for the sliding mode dynamics.Then,for deterministic Markov jump systems,the potential connection between system transferring and the stationary distribution of the Markov chain is analyzed.Moreover,a new sliding mode bumpless transfer control scheme is proposed,which can mitigate the limitations of existing bump-less transfer schemes.Further,the above new sliding mode bumpless transfer control scheme is extended to discrete Markov jump uncertain systems.Besides,the possible difficulties in capturing the system state in engineering practice are fully considered when designing a new strategy.Then an output-based switching function is chosen and an out-put feedback sliding mode controller is designed.The numerical simulation verifies the feasibility of the proposed sliding mode bumpless transfer control strategy.