The topics of source seeking and Newton-based extremum seeking have flourished, independently, but never combined. We present the first Newton-based source seeking algorithm. The algorithm employs forward velocity tuning, as in the very first source seeker for the unicycle, and incorporates an additional Riccati filter for inverting the Hessian inverse and feeding it into the demodulation signal. Using second-order Lie bracket averaging, we prove convergence to the source at a rate that is independent of the unknown Hessian of the map. The result is semiglobal and practical, for a map that is quadratic in the distance from the source. The paper presents a theory and simulations, which show advantage of the Newton-based over the gradient-based source seeking.

翻译：源搜索与基于牛顿法的极值搜索这两个主题虽各自蓬勃发展，却从未被结合过。本文首次提出基于牛顿法的源搜索算法。该算法沿用了最早针对独轮车的源搜索器中的前进速度调节方法，并额外引入一个黎卡提滤波器用于估计黑塞矩阵的逆，并将其注入解调信号。利用二阶李括号平均化方法，我们证明该方法能以与地图未知黑塞矩阵无关的速率收敛至源点。该结果对于与源点距离呈二次关系的地图具有半全局性和实用性。本文通过理论推导与仿真实验，展示了基于牛顿法的源搜索相比梯度法的优势。