Research On Asymptotic Synchronization Of Reaction-diffusion Systems Based On Several Types Of The Hybrid Control Strategies

Since the synchronization was found in the chaotic systems in the 80s of the last century,the research of chaotic synchronization mechanism and con-trol methods has been widespread concerned.Chaotic synchronization has been widely used in the field of secure communication,signal encyption and so on.It is an important research direction to design chaotic synchronization scheme using advanced control theory.Compared with finite dimensional ordinary differential systems,reaction diffusion systems have more complex dynamical behaviors,and can provide more information carriers.The syn-chronization control of reaction diffusion systems has become an import,ant part of chaotic synchronization.In this thesis,the asymptotic synchroniza-tion of reaction diffusion neural networks with Dirichlet boundary conditions has been considered via two kinds of discontinuous control strategies:inter-mittent and impulsive control.In addition,the asymptotic synchronization scheme for a class of Lipschitz nonlinear systems is designed by using reac-tion diffusion system as the driving force.By analyzing the driving mech-anisms,this thesis aims to develop the practical and effective hybrid syn-chronization strategies,analyze the relationship between driving mechanism,coupling strength and synchronization performance in a quantitative manner,and establish the parametric design methods for hybrid synchronization con-troller.The main results derived in this thesis are listed as follows:(1)The intermittent H? synchronization problem for a class of reaction-diffusion neural networks is studied.A switching-time-dependent Lyapuvoy function is introduced to analyze the exponential stability and L2-gain per-formance of the synchronization error dynamics.Given the switching mode,a criterion for designing H? synchronization controller is proposed in terms of linear matrix inequalities.Different from the previous works,it is allowed that the response system is subject to external disturbance,and both the con-trol period and the control width may be variable.(2)The synchronization problem of two identical reaction-diffusion neu-ral networks with Dirichlet boundary conditions and mixed delays is dis-cussed via periodically intermittent control.A novel piecewise exponential-type Lyapunov function based method has been introduced to analyze the stability of the synchronization error system.Compared with the Lyapunov functional based analysis method in the previous works,the Lyapunov-Razu-mikhin based method can provide the subtle estimates on the decay/divergent rate of solutions of error system during closed/open-loop mode,and the re-striction on the derivatives of discrete delays is also reduced.An improved synchronization result is derived.Based on the obtained synchronization cri-terion,the design problem of synchronization controllers is translated into the solution of a set of LMIs by using matrix transformation technique.(3)The impulsive H? synchronization analysis of reaction-diffusion neural networks with discrete and distributed delays is considered.It is assumed that the output information of the drive system is only available at discrete instants,and the dynamics of the response system are subject to external disturbance.Based on impulse-time-dependent Lyapunov func-tion/functional methods and LMI formulation,two types of impulsive syn-chronization schemes have been proposed.The first type imposes no any constraint on the discrete-delay derivative.The second type needs the restric-tion that the derivative of the discrete-delay is less than one but can provides less conservative synchronization result especially for the constant discrete-delay case.Based on the proposed impulsive synchronization criterion,the synchronization impulsive controller is designed,which can guarantee a pre-scribed L2-gain level of the synchronization error systems.(4)The synchronization problem of a class of Lipschitz nonlinear sys-tems driving by the reaction diffusion systems is discussed.Applying the stabilizing role of reaction diffusion term to achieve the complete synchro-nization of the ODE system is proposed.Firstly,ODE-PDE coupled system is transformed into the system with Dirichlet boundary conditions through the integral transform.The boundary controller is obtained by solving the kernel functions.Further,it is proved that the error system is exponential-ly stable by applying the weighted Lyapunov function and convex technique of exponential function.Thus,the considered Lipschitz system achieve the complete synchronization.