Newton-based extremum seeking for a static map coupled with a diffusion PDE at an arbitrary interior point
Newton-based extremum seeking for a static map coupled with a diffusion PDE at an arbitrary interior point
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DOI：
10.1109/iccia52082.2021.9403567
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
P. Nikdel;F. Sheikholeslam;M. Zekri;M. Ghadiri-Modarres
中科院分区：
文献类型：
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作者：
P. Nikdel;F. Sheikholeslam;M. Zekri;M. Ghadiri-Modarres
本文提出了一种基于牛顿的求解未知静态映射与扩散偏微分方程耦合的极值问题的方法。与以往的作品中，优化发生在零边界的扩散PDE，本文认为一个更一般的情况下，优化可以发生在任意内部点的扩散PDE。首先，设计加性和乘性抖动信号以提供平均意义上的映射的梯度和Hessian的估计。然后，将误差系统表示为一阶常微分方程与内点扩散偏微分方程的耦合，设计了一个显式动态反馈控制律来镇定误差系统，并利用Backstepping变换和无穷维平均定理证明了该方法的局部指数收敛性.最后给出了一个仿真例子来说明理论结果。
In this paper the Newton-based extremum seeking for an unknown static map which is coupled with a diffusion partial differential equation (PDE) is presented. In contrast with previous works where optimization takes place at the zero boundary of the diffusion PDE, this paper considers a more general case where the optimization can take place at an arbitrary interior point of the diffusion PDE. First, the additive and multiplicative dither signals are designed to provide the estimations of the gradient and Hessian of the map in the average sense. Then, the error system is formulated as a first-order ordinary differential equation (ODE) coupled with a diffusion PDE at an interior point and an explicit dynamic feedback law is designed for stabilizing it. By using the backstepping transformation and infinite dimensional averaging theorem, it is shown that the proposed scheme achieves local exponential convergence to a neighborhood of the extremum. A simulation example is given to illustrate the theoretical results.