一类不确定热方程自适应边界控制  

Adaptive Boundary Control for a Class of Uncertain Heat Equations

作　　者：李健[1] 刘允刚[1] 

机构地区：[1]山东大学控制科学与工程学院,济南250061

出　　处：《自动化学报》2012年第3期469-473,共5页Acta Automatica Sinica

基　　金：国家自然科学基金(60974003;61143011);教育部新世纪优秀人才支持计划(NCET-07-0513);教育部科学技术研究重点项目(108079);山东省杰出青年基金(JQ200919);山东省科技发展计划(2004GG4204014);山东省优秀中青年科学家奖励基金(2007BS01010);山东大学自主创新基金(2009JQ008)资助~~

摘　　要：研究了一类含有不确定控制系数和边界扰动的热方程自适应状态反馈边界控制设计问题.通过Lyapunov方法,显式地得到了仅需系统边界状态信息的自适应控制器.证明了闭环系统状态是L2[0,1]稳定的,特别是当边界扰动消逝时,该状态收敛到0.此外,通过灵活选取参数调节律的初始条件,适当放宽了相关文献中相容性条件对系统初始条件的限制.仿真算例验证了本文方法的有效性.This paper investigates the adaptive state-feedback boundary control design for a class of heat equations with uncer- tain control coefficient and boundary disturbance. By Lyapunov method, the desirable controller is explicitly constructed, which only needs the boundary state of the system. It is shown that the closed-loop system state is L2 [0, 1] stable, and particularly, the state converges to zero when the boundary disturbance van- ishes. Moreover, by skillfully choosing the initial condition of parameter updating law, the restriction on the initial condition of the system is moderately relaxed, which is usually described by the so-called compatible condition in the related literature. A simulation example is presented to illustrate the effectiveness of the proposed method.

关 键 词：自适应镇定 不确定控制系数 边界扰动 边界控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]