Adaptive stabilization for ODE systems coupled with parabolic PDES
Adaptive stabilization for ODE systems coupled with parabolic PDES
复制标题
与抛物线 PDES 相结合的 ODE 系统的自适应稳定
DOI：
10.1007/s11424-016-5094-4
复制
发表时间：
2016-05
影响因子：
2.1
通讯作者：
LIU Yungang
中科院分区：
文献类型：
--
作者：
LI Jian;LIU Yungang
研究了具有抛物型偏微分方程组的常微分方程组的自适应镇定问题。不确定性/未知因素的存在和子系统之间的耦合使得所研究的系统与现有文献中的系统有本质的不同，从而在控制设计中引入了更多的技术障碍。在相关文献的启发下，首次引入了具有适当核函数的可逆无限维逆推变换，将原系统转化为新的系统，从而使控制设计变得更加方便。值得指出的是，由于核函数满足的核方程是耦合的，而不是级联的，所以所需的核函数比相关文献的核函数更难推导。然后，利用Lyapunov方法和动态补偿技术，成功地构造了一个自适应镇定控制器，该控制器保证了闭环系统的所有状态都是有界的，而原始系统状态收敛到零。最后，给出了仿真算例，验证了该方法的有效性。
This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs. The presence of the uncertainties/unknonws and the coupling between the subsystems makes the system under investigation essentially different from those of the existing literature, and hence induces more technique obstacles in control design. Motivated by the related literature, an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one, from which the control design becomes much convenient. It is worthwhile pointing out that, since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded, the desirable kernel functions are more difficult to derive than those of the closely related literature. Then, by Lyapunov method and a dynamics compensated technique, an adaptive stabilizing controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converging to zero. Finally, a simulation example is provided to validate the proposed method.