Design and stability analysis of multivariate extremum seeking with Newton method

This paper proposes a multivariate extremum seeking with the Newton method (ES-NM) to improve the control performance for multivariable static and dynamic systems. The structure of the proposed ES-NM is designed to speed up the convergence of the scheme without increasing the oscillation. The influence of unknown Hessian matrix on the convergence speed existed in conventional methods is effectively eliminated in the proposed ES-NM approach. The stability analysis of the proposed ES-NM is given in detail for static and dynamic systems. Comparisons to the existing Gradient based extremum seeking control (ESC) and the Newton based ESC reveal that the proposed ES-NM has a higher probability of improving the convergence speed as well as reducing the chattering performance. Simulation results show advantages of the proposed ES-NM by comparing the multivariate Gradient based and Newton based ESC.