Adaptive stabilisation for uncertain coupled PDE–ODE systems
Adaptive stabilisation for uncertain coupled PDE–ODE systems
复制标题
DOI：
10.1080/00207179.2015.1006682
复制
发表时间：
2015-01
影响因子：
2.1
通讯作者：
Jian Li;Yungang Liu
中科院分区：
文献类型：
--
作者：
Jian Li;Yungang Liu
研究了一类具有参数不确定性的偏微分方程-常微分方程耦合系统的自适应镇定问题。不确定性的存在使得所研究的系统与现有文献中的系统存在本质上的差异，并且导致现有方法的不可行性。在前人工作的启发下，本文首先引入了一种无限维回溯变换，将原系统转化为关键目标系统，从而为控制设计和性能分析提供了方便。然后，利用Lyapunov方法和一些自适应技术，成功地构造了一个自适应镇定控制器，保证了闭环系统的所有状态都是有界的，而系统的原始状态收敛于零。通过仿真实例验证了该方法的有效性。
The adaptive stabilisation is investigated for a class of coupled partial differential equation–ordinary differential equation systems with parametric uncertainties. The presence of the uncertainties makes the systems under investigation essentially different from those in the existing literature, and moreover it results in the incapability of the existing methods. Motivated by the related works, an infinite-dimensional backstepping transformation is first introduced to transform the original system into a pivotal target system, which makes the control design and performance analysis much convenient. Then, by utilising Lyapunov method and some adaptive techniques, an adaptive stabilising controller is successfully constructed, which guarantees that all the closed-loop system states are bounded while the original system states converge to zero. A simulation example is provided to validate the proposed method.