Newton Nonholonomic Source Seeking for Distance-Dependent Maps

TL;DR

This paper introduces the first Newton-based source seeking algorithm that uses a Riccati filter and velocity tuning, achieving convergence independent of the unknown Hessian, with proven theory and simulation results.

Contribution

It combines Newton-based extremum seeking with source seeking, introducing a novel algorithm that converges efficiently for quadratic maps.

Findings

Convergence rate is independent of the unknown Hessian.

The Newton-based method outperforms gradient-based approaches.

The algorithm is practical and theoretically grounded.

Abstract

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.