Protocol-Based Analysis And Control For Semi-Markov Jump Systems

Markov jump system is a highly effective tool for describing sudden changes in structure and parameters,and it finds wide applications in various fields,including aerospace,smart grid,and robotics systems.However,the current dwell time in Markov jump systems follows a memoryless exponential distribution,which means that the transition probability is timeinvariant.This limitation restricts its practical application.To address this issue,semiMarkovian processes have been proposed.These processes allow for arbitrary publication of the dwell times,making the study of semi-Markovian jump systems of significant theoretical significance and application.Moreover,event-triggered protocols have become popular due to their ability to save computational resources and maintain the desired control performance,overcoming the shortcomings of traditional time-triggered protocols.Hence,this study aims to investigate the analysis and control issues of semi-Markov jump systems by optimizing event-triggered protocols.(1)The asynchronous control problem for a particular type of semi-Markov switching system in the presence of singular perturbation is addressed,with the aim of reducing network resource occupation.To achieve this goal,an improved triggering protocol is skillfully established by adopting two auxiliary offset variables.This protocol has the advantage of arranging information transmission with greater degrees of freedom compared to existing protocols,which helps to reduce communication frequency while maintaining control performance.In addition to the reporting hidden Markov model,a nonhomogeneous hidden semi-Markov model is conducted to tackle mode mismatch between the systems and controllers.Using Lyapunov techniques,parameter-dependent sufficient conditions are devised to ensure stochastic stability subject to a predetermined performance.To demonstrate the viability of the proposed methodology,a numerical example and the tunnel diode circuit model are provided.(2)The output-feedback control problem for general semi-Markov jump systems with a memory dynamic event-triggered protocol is discussed.A novel framework of semi-Markov process subject to a higher level deterministic switching signal is constructed,based on the average dwell time strategy.In this framework,the Markov renewal process is nonhomogeneous.To improve communication efficiency and control performance,a novel dynamic memory event-triggered protocol is proposed,resulting in a time-delay system.To ensure the mean-square exponential stability of the closed-loop system,some parameter dependent sufficient criteria are forwarded by considering an asynchronous memory-based output feedback control law.The asynchronization can be modeled by a nonhomogeneous hidden semi Markov model.Finally,the effectiveness and applicability of the presented approach are demonstrated by two examples.(3)The sliding mode control problem for singular semi-Markov jump systems,using a novel dynamic-memory event-triggered protocol is addressed.A deterministic switching signal was developed based on the average dwell time strategy,to adjust the variation of the semi-Markov chains.To enhance transmission efficiency and achieve better control performance,a novel dynamic-memory triggering condition is proposed.This condition implements both historical transmitted data and two auxiliary dynamic variables.Based on the proposed protocol and Lyapunov theory,some parameter dependent sufficient criteria are established to guarantee mean-square exponential stability and strictly dissipative performance,and the desired memory-based sliding mode controller is designed.Finally,two simulation examples are presented to verify the effectiveness of the proposed methodology.