一类空间非因果关系反应扩散方程的边界控制

运用Backstepping方法研究了一类空间非因果关系的反应扩散方程的稳定性问题,该系统的温度与整个空间有关系,而不是仅仅与空间中的某一点有关,因此,给控制器的设计带来了难度.为设计反馈控制器,首先,选用边界反馈控制的Backstepping方法进行设计;其次,在设计过程中增加核函数个数,引入改进后的Volterra型积分变换,再采用求解偏微分方程的变量分离法求解出核函数;最后,找到Volterra变换的逆变换,利用Volterra变换及其逆变换的有界性,可证明控制器的有效性.

Stabilization of a Spatially Non-Causal Reaction-Diffusion Equation by Boundary Control

Stabilization of a reaction-diffusion equation, in which the heat source depends on the temperature of the whole space, is considered by boundary control. The system is more complicated. For the new system, a new Volterra transformation is introduced, in which there are two kernels. Through a solution of separated variables, the exact solutions of kernels are obtained, and a control law is obtained specifically. The inverse transformation is derived, and stability of the closed loop system established via the boundedness of transformation and the inverse transformation.