| In the real life, systems are always subject to stochastic disturbances from the surrounding environment, which have an important impact on properties of systems. In addition, states of some systems depend on not only the time, but also the spatial position. When systems appear in the nonuniform space, the diffusion phenomenon is avoidable. Generally speaking, systems are not always isolated, but they couple with each other. Under the extern input, systems can have the same states, say, achieving synchronization. According to the required time to achieve synchronization, the synchronization is divided into asymptotic synchronization and finite-time synchronization. Asymptotic synchronization needs infinite time to achieve synchronization, while that is finite time for finite-time synchronization. Differing from ordinary differential equation, the boundary control is an effective control strategy for coupled reaction-diffusion systems. For coupled reaction-diffusion systems, boundary controllers and finite-time synchronization controllers are designed to force systems to achieve the asymptotic synchronization and finite-time synchronization, respectively.In Chapter 2, asymptotic synchronization for coupled reaction-diffusion systems is considered, including deterministic and stochastic coupled reaction-diffusion systems. Asymptotic synchronization for coupled reaction-diffusion systems with Neumann boundary conditions and mixed boundary conditions is studied, respectively. Boundary controllers are designed. By using Lyapunov-Krasovshii functional and LMI inequality, conditions that systems achieve synchronization are obtained. When systems are affected by stochastic disturbances, mean asymptotic synchronization for stochastic coupled reaction-diffusion systems with Neumann boundary conditions and mixed boundary conditions is studied, and conditions guaranteeing mean asymptotic synchronization are obtained. To illustrate the effectiveness and correctness of results we get, examples are given.In Chapter 3, finite-time synchronization for coupled reaction-diffusion systems is investigated, including deterministic and stochastic coupled reaction-diffusion systems. Finite-time synchronization controllers are designed for deterministic coupled reaction-diffusion systems, and the condition guaranteeing finite-time synchronization is obtained. Then, finite-time synchronization for stochastic coupled reaction-diffusion systems is considered. At last, examples are given to show the effectiveness of our results.Finally, a brief conclusion is given to summarize our work and put forward the plan in the future. |
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