Research On State Estimation And Control Of Jump Systems With Diffusion Terms

In engineering practice,the parameters and structure of networks may encounter unpredictable changes arising from variations among different operation points during a nonlinear process,the switching among economic scenarios,component failures,or other reasons,jump system can be used to describe this phenomenon.Furthermore,in many jump systems,such as electric circuits,diffusion phenomenon occurs inevitably when electrons move in non-uniform magnetic field,so it is necessary to introduce diffusion term into jump systems.Jump systems with diffusion terms are represented by partial differential equations with initial and boundary conditions,and can be employed to model plenty of physical processes having an infinite-dimensional feature and spatiotemporal dynamics,has been widely used in secure communication,information classification,robotics and so on.Based on the Lyapunov stability theory,using the linear matrix inequality techniques,for a class of jump partial differential system,from the performance index,the communication channel delay to study the control and estimation problem,the concrete contents are as follows:1.Consider the non-fragile dissipative state estimation problem for semi-Markov jump inertial neural networks with reaction-diffusion terms.A semi-Markov jump model is used to describe the stochastic jump parameters in networks.Different from the invariable transition probabilities in the traditional Markov jump systems,the transition probabilities of the semi-Markov jump systems rely on the stochastic sojourn-time.Accordingly,the Weibull distribution taking the place of the exponential distribution in this paper is adopted for the sojourn-time of each mode in the system.Firstly,by utilizing an applicable vector substitution,the second-order differential system could be converted into the first order one.Afterwards,via constructing a seemly Lyapunov function for the semi-Markov inertial neural networks and adequately taking advantage of the peculiarities of cumulative distribution functions,some sufficient conditions with less conservatism are constructed to assure that the estimation error system is strictly（R₁,R₂,R₃）--dissipative stochastically stable.Based on these conditions,mode-dependent estimator gains are designed.Finally,a numerical example is proposed to validate the availability of the provided approach.2.Consider a class of semi-Markov jump distributed parameter systems and study its adaptive event-triggered control issue under Dirichlet boundary conditions.An event-triggered transmission scheme,whose threshold function can be adaptively adjusted,is established to decrease the frequency of data transmission.Simultaneously,the utilization of limited network bandwidth resources is also improved due to plenty of unnecessary packets being discarded before accessing the network.Furthermore,the jumping of stochastic parameters in networks can be described by a semi-Markov jump model,in which the sojourn-time is considered subject to the Weibull distribution instead of the exponential distribution.Based on the aforesaid discussions,a mode-dependent controller is designed under an adaptive event-triggered scheme.Whereafter,some criteria are constructed based on the Lyapunov stability theory to guarantee stochastic stability and a prescribed（?）performance of the system.Ultimately,two simulation examples are provided to verify the feasibility of the proposed controller design approach.3.Research the passive boundary control problem for continuous-time hidden Markov neural networks with reaction-diffusion terms via a detector-based method.The abrupt variations of parameters and structure in networks are modeled as a continuous-time hidden Markov jump model encompassing the hidden state and the observed state,in which the hidden state expresses the kinetics of the actual system,and cannot be known precisely,but instead,it can be observed via a detector.A distinctive feature of the detector-based approach is that it comprises,such as cases with complete information,no information,etc.,and enables us to observe in a unitive manner.In this paper,we firstly introduce the mathematical model of a continuous-time hidden Markov jump process.Further,a boundary controller relying on the observation mode afforded by the detector is devised to stochastically stabilize the closed-loop system.Whereafter,some criteria in the form of linear matrix inequalities are constructed based on the Lyapunov stability theory to achieve a prescribed passive performance of the system.Ultimately,we verify the proposed approach by two simulation examples.