Second-Order Newton-Based Extremum Seeking for Multivariable Static Maps

A second-order Newton-based extremum seeking (SONES) algorithm is presented to estimate directional inflection points for multivariable static maps. The design extends the first-order Newton-based extremum seeking algorithm that drives the system toward its peak point. This work provides perturbation matrices to estimate the second- and third-order derivatives necessary for implementing the SONES. A set of conditions are provided for the probing frequencies that ensure accurate estimation of the derivatives. A differential Riccati filter calculates the inverse of the third-order derivative. The local stability of the new algorithm is proven for general multivariable static maps using averaging analysis. The proposed algorithm ensures uniform convergence toward directional inflection points without requiring information about the curvature of the map and its gradient. Simulation results show the effectiveness of the proposed algorithm.