【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.更多还原

【Abstract】 This paper investigates the adaptive state-feedback boundary control design for a class of heat equations with uncertain 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 vanishes.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.更多还原