Feedback control for a class of second order hyperbolic distributed parameter systems

Abstract

This paper deals with the problem of state feedback control for a class of the distributed parameter systems with the disturbance term. And the considered distributed parameter systems are composed of the second order hyperbolic partial differential equations. Two different classes of restrictions on the disturbance term are given, one is that the disturbance term satisfies the linear growth constraint condition to the state variables of the system, and the other is that the disturbance term obeys the bound constraint under the significance of L ₂. Based on a variable structure method, the state feedback controllers are obtained by means of constructing appropriate Lyapunov functional. The closed-loop systems are globally asymptotically stable on W ^1,2(0, 1) × L ₂(0, 1) space under the effect of the state feedback control laws. Simulation results illustrate the effectiveness of the proposed method.

摘要

创新点

研究一类带扰动项的分布参数系统的状态反馈控制问题, 该类分布参数系统由二阶双曲型偏微分方程构成。 通过构建一种新的 Lyapunov 泛函, 基于变结构方法, 设计得到一种新的变结构状态反馈控制律。 当该类控制律作用于系统时, 若扰动项满足线性增长性条件, 则闭环系统的强解于W1,2(0,1)*L2(0,1)空间内全局渐近稳定; 若扰动项满足有界性约束条件, 则闭环系统的广义解于W1,2(0,1)*L2(0,1)空间内全局渐近稳定。 当扰动项为零时, 已有的变结构控制方法, 获得的结论为: 广义解意义下, 全局渐近稳定。 由于本文采用了新的 Lyapunov 泛函及反馈控制器, 当扰动项为零时, 得到的结论为: 强解意义下, 全局渐近稳定, 由此改进了已有的相应结论。