Newton-based Extremum Seeking under Actuator and Sensor Delays∗

In addition to the gradient based extremum seeking for delay systems presented in a companion paper, we derive here the control design and analysis for scalar Newtonbased extremum seeking subject to input-output delays. differently from the previous work, a new predictor with a perturbation-based estimate of the Hessian's inverse is incorporated in the closed-loop such that the convergence rate of the real-time controller can be made userassignable, rather than being dependent on the unknown Hessian of the static nonlinear map to be optimized. Exponential stability and convergence to a small neighborhood of the unknown extremum point can be obtained. This result is rigorously achieved by using backstepping transformation and averaging in in?nite dimensions. A numerical example is given to illustrate the effectiveness of the proposed predictor based extremum seeking for time-delay compensation.