Multivariable Newton-based extremum seeking

Abstract

We present a Newton-based extremum seeking algorithm for the multivariable case. The design extends the recent Newton-based extremum seeking algorithms for the scalar case and introduces a dynamic estimator of the inverse of the Hessian matrix that removes the difficulty with the possible singularity of a possible direct estimate of the Hessian matrix. The estimator of the inverse of the Hessian has the form of a differential Riccati equation. We prove local stability of the new algorithm for general nonlinear dynamic systems using averaging and singular perturbations. In comparison with the standard gradient-based multivariable extremum seeking, the proposed algorithm removes the dependence..