Finite-time Boundary Control Of Several Reaction-diffusion Systems

States of some systems depend on not only the time,but also the spatial position.When these systems appear in a nonuniform space,the diffusion phenomenon is easily to occur.Finite-time stabilization of reaction-diffusion systems derives from industrial need,unlike asymptotical stability,finite-time stabilization requires the state of a system to remain in a given bounded region in a finite time.In the real life,time-delays are inevitable and systems' properties are also always subject to stochastic disturbances from the surrounding environment.Boundary control is an effective method to achieve finite-time stabilization of reaction-diffusion systems.Except certain interference factors,some uncertain interference can also play a terrible role in the state of system,H-infinity performance is an effective index to show the ability of resisting external disturbances for disturbed systems.It is of great theoretical significance and application value to study the above problems.In Chapter 2,finite-time stabilization control for reaction-diffusion systems is considered.In order to better illustrate the advantage of boundary control,we first adopt a full-domain controller to achieve finite-time stabilization.Then,by constructing appropriate Lyapunov functional and making use of Poincaré inequality,boundary controllers for Neumann boundary conditions and mixed boundary conditions are designed respectively,and sufficient criteria are derived for finite-time stabilization.Finally,when some uncertain parameters exist in systems,we study the robust finite-time stabilization of reaction-diffusion systems with parameters.In Chapter 3,finite-time stabilization and H-infinity stabilization of delay reaction-diffusion systems are considered.In consideration of finite-time stabilization for delay reaction-diffusion systems,by designing effective full-domain controller and boundary controller,respectively,we derive the sufficient conditions to ensure finite-time stabilization of systems under two controllers.When an non-white additive noise enters the considered system,H-infinity stabilization control is considered under that circumstances.Because of stochastic modeling's extensive application in the field of engineering and finance,in Chapter 4,we consider the finite-time stabilization in probability of stochastic reaction-diffusion systems under two boundary conditions.By using Lyapunov-Krasovskii functional and It? formula,the sufficient conditions are derived to ensure finite-time stabilization in probability of stochastic reaction-diffusion systems.Finally,a brief conclusion is given to summarize our work and put forward the ideas in the following.