| Reaction-diffusion systems(RDSs)can describe many phenomena in real life,such as the diffusion of biological population,the convection diffusion of river pollutants,the diffusion of infectious diseases,heat conduction and so on.It is of great practical value to effectively control this kind of systems.Distributed control and boundary control are two control methods of RDSs.Distributed control requires the controller to be placed at each point in the spatial region where the system is located.Boundary control is easier to be realized in practice because it only requires the controller to be placed at the boundary of the spatial region.Therefore,it is of theoretical and applied value to research boundary control of RDSs.In this thesis,continuous boundary controller and intermittent boundary controller are designed for several kinds of RDSs,and the effects of diffusion coefficient,spatial region length,time delay,control gain and intermittent control time ratio on the dynamic performances of the considered systems are analyzed.The main research contents are as follows:Most of the existing boundary controllers for RDSs are continuous controllers,and this means that the controllers need to work continuously,but the results of discontinuous boundary controllers are few.Two discontinuous boundary control strategies,intermittent boundary controller and observer-based intermittent boundary controller,are proposed in this thesis.The exponential stability of RDSs is studied,and the effects of diffusion coefficient,spatial region length and intermittent control time ratio on the stability of the considered system are analyzed.In addition,it is proved that the observer-based intermittent boundary controller is feasible for the uncertain RDSs.Backstepping method is a mature solution for the boundary control of deterministic RDSs,but it is difficult to be extended to RDSs with stochastic factors,which also leads to few results about the boundary control of RDSs with stochastic factors.The state-dependent boundary controller and observer-based boundary controller are given for stochastic RDSs in this thesis.By the Lyapunov functional method,sufficient conditions on the exponential stability are obtained and a conclusion is pointed out that the exponential convergence rate can be adjusted by the control gain.In addition,a boundary controller is designed to study the mean square finite-time stability of stochastic RDSs,and the controller is applied to the robust mean square finite-time stability of uncertain stochastic RDSs.Time delay is universal in the process of information transmission of neural networks,but there are few results about the boundary control of delayed reaction-diffusion neural networks.Cohen-Grossberg neural network is a general neural network,which can be transformed into recursive neural network,Hopfield neural network,cellular neural network and other models by selecting appropriate parameters.The design schemes of continuous boundary controller and aperiodically intermittent boundary controller are presented for reaction-diffusion Cohen-Grossberg neural networks with delay and stochastic factors.Delay-dependent sufficient conditions are obtained to ensure the mean square exponential stability.The effects of time delay and diffusion coefficient on stability are analyzed,and the range of intermittent control time ratio is given.Fractional-order systems have genetic and memory properties,which can better describe the problems of viscoelasticity and fluid mechanics,and have the practical application value.However,there exist few research results on boundary control for fractional RDSs.This thesis study the fractional reaction-diffusion neural networks finally.A state-dependent boundary controller and an observer-based boundary controller are given and sufficient conditions for achieving Mittag-Leffler stability are obtained.Then,the design schemes of intermittent boundary controller and observer-based intermittent boundary controller are given for delay fractional reaction-diffusion neural networks,and time-dependent sufficient conditions are obtained to realize the synchronization.All the theoretical results and the effectiveness of the controller are verified by numerical examples in the corresponding chapters. |
