Newton-like extremum-seeking part I: Theory

In practice, the convergence rate and stability of perturbation based extremum-seeking (ES) schemes can be very sensitive to the curvature of the plant map. This sensitivity arises from the use of a gradient descent adaptation algorithm. Such ES schemes may need to be conservatively tuned in order to maintain stability over a wide range of operating conditions, resulting in slower optimisation than could be achieved for a fixed operating condition. This can severely reduce the effectiveness of perturbation based ES schemes in some applications. It is proposed that by using a Newton-like step instead of a more typical gradient descent adaptation law, then the behaviour of the ES scheme near an extremum will be independent of the plant map curvature. In this paper, such a Newton-like ES scheme is developed and its stability and convergence properties are explored.