Stochastic Extremum Seeking for Dynamic Maps with Delays

Damir Rusiti1, Giulio Evangelisti2, Tiago Roux Oliveira3, Matthias Gerdts4, Miroslav Krstic5

  • 1University of the Federal Armed Forces Munich
  • 2Technical University of Munich
  • 3State University of Rio de Janeiro
  • 4University of Munchen
  • 5University of California, San Diego

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Invited Session

Sessions

10:00 - 12:00 | Mon 17 Dec | Splash 5-6 | MoA15

Estimation and Control of PDE Systems I

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Abstract

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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