Damir Rusiti1, Giulio Evangelisti2, Tiago Roux Oliveira3, Matthias Gerdts4, Miroslav Krstic5
10:00 - 12:00 | Mon 17 Dec | Splash 5-6 | MoA15
We present a Newton-based extremum seeking algorithm for maximizing higher derivatives of unknown maps in the presence of time delays. Different from previous works about extremum seeking for higher derivatives, we employ stochastic instead of periodic perturbations, allow arbitrarily long output delays as well as dynamic maps. We incorporate a predictor feedback with a perturbation-based estimate for the Hessian's inverse using a differential Riccati equation and stochastic demodulation signals making the convergence rate user-assignable. Furthermore, exponential stability and convergence to a small neighborhood of the unknown extremum point is achieved for locally quadratic derivatives by using a backstepping transformation and averaging theory in infinite dimensions for stochastic systems. We also present simulations to highlight the effectiveness of our predictor-feedback scheme.
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