Extremum Seeking Feedback With Wave Partial Differential Equation Compensation
Extremum Seeking Feedback With Wave Partial Differential Equation Compensation
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DOI：
10.1115/1.4048586
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发表时间：
2021-04
影响因子：
1.7
通讯作者：
T. R. Oliveira;M. Krstić
中科院分区：
文献类型：
--
作者：
T. R. Oliveira;M. Krstić
本文解决了静态地图标量极值搜索（ES）中波致动器动力学的补偿问题。到目前为止，ES 文献中尚未考虑由波型偏微分方程（PDE）描述的无限维系统。最初提出了一种使用反步方法和诺依曼驱动的基于分布式参数的控制律。通过采用李亚普诺夫-克拉索夫斯基泛函和无限维平均理论，可以保证局部指数稳定性以及实际收敛到未知极值点的任意小邻域。此后，还讨论了狄利克雷驱动的波动方程的推广、反稳定波偏微分方程以及延迟波偏微分方程级联的设计。数值模拟说明了理论结果。 [DOI：10.1115/1.4048586]
This paper addresses the compensation of wave actuator dynamics in scalar extremum seeking (ES) for static maps. Infinite-dimensional systems described by partial differential equations (PDEs) of wave type have not been considered so far in the literature of ES. A distributed-parameter-based control law using back-stepping approach and Neumann actuation is initially proposed. Local exponential stability as well as practical convergence to an arbitrarily small neighborhood of the unknown extremum point is guaranteed by employing Lyapunov–Krasovskii functionals and averaging theory in infinite dimensions. Thereafter, the extension for wave equations with Dirichlet actuation, antistable wave PDEs as well as the design for the delay-wave PDE cascade are also discussed. Numerical simulations illustrate the theoretical results. [DOI: 10.1115/1.4048586]