Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs
Output Feedback Boundary Control of a Heat PDE Sandwiched Between Two ODEs
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DOI：
10.1109/tac.2019.2901704
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发表时间：
2019-02
影响因子：
6.8
通讯作者：
Ji Wang;M. Krstić
中科院分区：
文献类型：
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作者：
Ji Wang;M. Krstić
本文提出了一类常微分方程(ODE)-热偏微分方程(PDE)-ODE耦合系统的指数镇定设计，其中控制驱动仅作用于一个ODE。在状态反馈控制律和仅使用一次PDE边界测量估计PDE和两个ODE状态的观测器中，采用了PDE反演和ODE反演的组合。在状态反馈控制律和观测器的基础上，提出了输出反馈控制律。通过李雅普诺夫分析证明了闭环系统的指数稳定性和控制律的有界性和指数收敛性。最后，通过数值仿真验证了该方法对“三明治”系统的有效性。
We present designs for exponential stabilization of an ordinary differential equation (ODE)-heat partial differential equation (PDE)-ODE coupled system where the control actuation only acts in one ODE. The combination of PDE backstepping and ODE backstepping is employed in a state feedback control law and in an observer that estimates PDE and two ODE states using only one PDE boundary measurement. Based on the state feedback control law and the observer, the output feedback control law is then proposed. The exponential stability of the closed-loop system and the boundedness and exponential convergence of the control law are proved via Lyapunov analysis. Finally, numerical simulations validate the effectiveness of this method for the “sandwiched” system.