Control And Filtering For Singular Markov Jump LPV Systems Under Event-triggered Strategy

Markov jump systems are the systems with random switching rules consisting of multiple subsystems.And they can remarkably describe systems with random parameter changes,such as internal component failures and operating point changes.As a general form of Markov jump systems,the sojourn-time of semi-Markov jump systems obeys more general time-varying distributions with memory,like Weibull distribution,Gaussian distribution.Considering the time-varying and nonlinear characteristics of the real system,they can be modelled as a linear parameter-varying(LPV)systems with unknown and measurable parameters.And LPV systems are widely used in missile automatic flights,turbofan engines and wind energy conversion systems,etc.However,with the increasing complexity of objects,the difficulty of system modeling has been greatly increased.And Markov jump systems can not matching the need of modeling,how to accurately describe the objects with time-varying random jump characteristics has become an urgent task.In such a context,the study of control and filtering for singular Markov jump LPV systems is of important theoretical and practical significance.Meanwhile,under the current trend of intelligence,the majority of signals are transmitted through the wireless channels.However,some problems inevitably arise through wireless channel,such as bandwidth limitations,transmission delays,data packet loss and network attacks,etc.Therefore,the introduction of wireless communication for the singular Markov jump LPV systems requires consideration of the above issues,which inevitable increases the complexity of analysis and synthesis.Actually,event-triggered transmission schemes have proven to be effective tools for saving limited bandwidth resources,while deception attacks as a more covert attack among many malicious attacks have become a common attack method for attackers.Up to now,the problem of dissipative stability for singular Markov jump LPV systems in the framework of event-triggered and network attacks has not been effectively solved,so it is necessary to study this problem.In this article,the stochastic admissibility problem for a class of singular Markov jump LPV systems with unknown transition rates is studied under the dynamic eventtriggered transmission strategy,including the design of asynchronous controllers and filters,the detection of network attacks,the analysis of dissipativity,and the design of asynchronous integral sliding mode law.The main works of the article are summarized as below.(1)The asynchronous controller is formulated for a class of singular Markov jump LPV systems under the dynamic event-triggered transmission strategy.The transition rates of the system are considered as both partially unknown and completely known.The dissipative and stochastic admissibility for the systems is analyzed by parameterdependent Lyapunov-Krasovskii functional.And the sufficient conditions of stochastic admissibility for singular Markov jump LPV systems with the desired dissipative performance have been given by the linear matrix inequalities(LMIs).The Hidden-Markovmodel has been employed to formulate the unobservable phenomena between modes of the asynchronous controllers and the original systems.The traditional static eventtriggered transmission strategy is improved to a dynamic version with internal dynamic variables and parameter-dependent weighting matrices.Finally,the numerical instance and resistance-inductance switch circuit system are considered to verify the feasibility of the designed scheme.(2)The asynchronous controller is formulated for a class of T-S fuzzy singular Markov jump LPV systems under the dynamic event-triggered transmission strategy.Unlike in(1),we attempt to employ the T-S fuzzy singular Markov jump LPV systems to describe the stochastic characteristics and nonlinear time-varying characteristics of nonlinear systems.And an asynchronous affiliation function is established for the T-S fuzzy systems.The transition rates of the systems are considered as partially unknown,completely known and completely unknown.The deception attacks are considered between the controller and the actuator,the plant and the controller,receptively.The triggered and control signals may be replaced with attack signals that is modeled as a smooth nonlinear function.Finally,the Lorenz chaotic systems and the truck-trailer systems are considered to explain the feasibility of the designed scheme.(3)The asynchronous sliding mode controller is formulated for a class of singular semi-Markov jump LPV systems under the dynamic event-triggered transmission strategy.Unlike in(1),the form of polyhedral is considered for LPV systems where the range of parameter variation is constrained within a finite vertex.The transition rate of the semi-Markovian jump system is considered as the fully known and partially unknown,which is modeled as the sum of known constants and unknown small variables,which does not need to be treated as an upper and lower bound.The occurrence of the deception attacks is considered at the controller input,and the attack signals is modeled as a nonlinear function with bounded intervals.The parameter-dependent and mode-dependent asynchronous integral-type sliding surfaces are designed,which reduce the conservatism of the system after reaching the sliding surface.The strictly dissipative and stochastic admissibility for the systems is analyzed by parameter-dependent Lyapunov-Krasovskii functional.The sufficient conditions of stochastic admissibility for the systems and the design of asynchronous sliding mode laws have been given by a set of LMIs.Finally,a simulation result of the multi-mode DC-motor has offered to verify the feasibility of the proposed scheme.(4)The asynchronous filter is formulated for a class of singular Markov jump LPV systems under the dynamic event-triggered transmission strategy.The asynchronous filter is constructed by a hidden-Markov-model and the deception attack occurs at the input of the filter.The dissipative and stochastic admissibility for the systems is analyzed by parameter-dependent Lyapunov-Krasovskii functional.And the sufficient conditions of stochastic admissibility for singular Markov jump LPV systems with the desired dissipative performance have been given by the LMIs.Finally,the numerical instance and resistance-inductance-capacitance switch circuit system are considered to verify the feasibility of the designed scheme.(5)The asynchronous attack detection filter is designed for nonlinear cyber-physical systems under the dynamic memory event-triggered transmission strategy.We attempt to employ the T-S fuzzy singular semi-Markov jump LPV systems to describe the stochastic characteristics and nonlinear time-varying characteristics of nonlinear systems.And an asynchronous affiliation function is established for the T-S fuzzy systems.The system is subject to the false data injection attacks and the multi-channel deception attacks at the physical end and filter input,respectively,i.e.,multiple channels may be subject to deception attacks.The dynamic memory event-triggered transmission strategy is proposed at the first time.The data buffer is added next to the event generator which allow more control signals to be obtained at key locations like the wave crest and trough,thus reaching steady state faster.The strictly dissipative and stochastic admissibility for the systems is analyzed by parameter-dependent Lyapunov-Krasovskii functional.And the sufficient conditions of stochastic admissibility for the systems with the desired strictly dissipative performance have been given by a set of LMIs to make the systems detect and alarm after the false data injection attacks.Finally,the feasibility of the designed scheme is verified via the networked truck-trailer reversing system.