具有Neumann边界的分布参数切换系统的容错控制

Fault-tolerant control for distributed-parameter switched systems with Neumann boundary conditions

本文研究了一类具有Neumann边界条件的分布参数切换系统的容错控制问题.当执行器失效或部分失效时,运用Lyapunov函数法和Green公式,获得了闭环切换系统混杂状态反馈容错控制器存在的充分条件.然后运用线性矩阵不等式将容错控制器设计问题转化为一组线性矩阵不等式求可行解的问题,因而可以借助MATLAB中线性矩阵不等式工具箱来完成.同时,运用Poincare不等式减少控制系统设计的保守性.最后通过数值算例,验证所提出设计方法的有效性.

We study the fault-tolerant control for a class of distributed parameter switched systems with Neumann boundary conditions. Under actuator failure or partial failure, the sufficient condition for the existence of a closed-loop switched fault-tolerant controller with hybrid state feedback is obtained based on Lyapunov function method and Green formula. By the linear matrix inequality （LMI） approach, the design of the fault-tolerant controller is converted into finding feasible solutions to a group of LMIs, which can be efficiently carried out by using MATLAB LMI toolbox. Simultaneously, Poincare inequality is used to reduce the conservativeness of the control system design. Finally, a numerical example validates the proposed design method.