Bounded Extremum Seeking for Single-Variable Static Map using State Transformation

Frederic Mazenc (1, 2) , Michael Malisoff (3) , Emilia Fridman (4)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 L2S - Laboratoire des signaux et systèmes
3 LSU - Louisiana State University
4 TAU - Tel Aviv University

We solve a gradient based bounded extremum seeking problem for single-variable static maps in the presence of time-varying piecewise continuous measurement uncertainty. Instead of using previously reported averaging-based methods, we introduce a new state transformation, allowing us to use new comparison function and generalized Lyapunov function approaches to obtain our ultimate bounds on the parameter estimation error. We illustrate significant advantages of our new method, including less restrictive conditions on the extremum seeking parameters, as compared with previous methods.

Mots clés: Extremum seeking; uncertainty; time-varying. Supported

Domaines: Mathématiques [math]

Frederic Mazenc, Michael Malisoff, Emilia Fridman. Bounded Extremum Seeking for Single-Variable Static Map using State Transformation. CDC 2024 - 63rd IEEE Conference on Decision and Control, Dec 2024, Milan, Italy. ⟨hal-04704546⟩