Boundary Control Of Several Kinds Of Markov Jump Reaction-diffusion Systems

Random mutation behavior generally exists in some engineering systems.For instance,device damage,random failures,or abrupt environmental changes often occur in the power systems,flight systems and communication systems,etc.Markov jump systems,as a special class of hybrid systems,have been widely used to characterize some practical systems with mutations.Diffusion is generally inevitable due to the inhomogeneity of density or concentration in different spatial domains.Therefore,Markov jump reaction-diffusion system has become one of the objects widely studied by scholars,and its control issue has also become a hot research topic at present.Since Markov jump reaction-diffusion systems have the characteristics of temporalspatial distribution,apart from the distributed control,boundary control is a economical and efficient method of controlling only at the boundaries of spatial domain.In light of its merits of low cost and easy implementation,boundary control is of great engineering significance in the road traffic control,chemical process control,biological population protection and river water pollution control,etc.However,the study of boundary control is more difficult than that of distributed control,since the control input is only reflected in the boundary conditions of the system.Based on the mode-dependent Lyapunov functional method,this dissertation investigates the specific problem of this kind of hybrid partial differential systems by utilizing stochastic analysis theory,and a series of boundary control theories for such systems are established.The specific work is as follows:Firstly,the boundary control of stochastic linear Markov jump reaction-diffusion systems is studied,and two cases of completely known and partially unknown transition probabilities of Markov chain are considered,respectively.Based on the boundary feedback control scheme,a criterion for the system to achieve asymptotic stability is established.When the system is subjected to external disturbances,the theory of H∞ boundary control is studied.Also,robust stabilization is extended for the parametric uncertain system,and the result of explicitly solving boundary control gains is given.Secondly,finite-time boundary stabilization for the stochastic nonlinear Markov jump reaction-diffusion systems is considered,and an efficient finite-time boundary control strategy is proposed.Based on this control strategy,the condition for the system to achieve finite-time boundedness is obtained.When transition rate information is partially unknown,we further study the finite-time boundedness problem in the case of partially unknown transition rates by free connection weighting matrices method,and analyze the relationship between the result in the case of partially unknown transition rates and the one in the case of completely known transition rates.Thirdly,this dissertation concerns with the asynchronous boundary control for the deterministic Markov jump reaction-diffusion neural networks.In response to the asynchronous behavior between the neural network modes and controller modes,a novel asynchronous boundary control design scheme is proposed.Based on this design scheme,sufficient criteria for stochastic finite-time boundedness and H∞performance under Neumann boundary conditions and mixed boundary conditions are established.At the same time,such kinds of neural networks with mixed time-varying delays are studied,and the discriminant condition that depends on time-delay information is given,which illustrates that parameters such as the upper bound of time-varying delays,the upper bound of time-varying delay derivatives,and the diffusion coefficient have great impact on the exponential stability of the system.Finally,asynchronous boundary stabilization problem is addressed for stochastic Markov jump reaction-diffusion systems.Based on a general hidden Markov model that considers partly unknown transition rates and partly unknown observation probabilities,two different design schemes for asynchronous boundary control are presented,namely distributed-output-based design scheme and boundary-output-based one.The results are obtained to ensure the mean square exponential stability with strictly dissipative performance,and the relationship between the noise intensity,the spatial domain and diffusion coefficient on the system performance is analyzed.The results obtained in this dissertation and the validity of the boundary control design are illustrated by numerical examples in the assigned chapter.