Abstract

Developed originally by Maurice Leblanc in 1922 and later advanced in the 1950s and 2000s, extremum-seeking (ES) control has long faced challenges with steady-state oscillations and biased convergence. This talk presents multivariable ES designs that achieve the first unbiased convergence of inputs to their optimal values, eliminating these oscillations and resolving a longstanding issue in classical ES. I will present two advanced designs: the unbiased extremum seeker (uES) with exponential unbiased convergence and the unbiased PT extremum seeker (uPT-ES) with user-assignable prescribed-time unbiased convergence. Unlike conventional extremum seekers that use persistent sinusoids leading to steady-state oscillations, the exponential uES utilizes an exponentially decaying perturbation amplitude for convergence and an exponentially growing demodulation signal to ensure unbiasedness. The unbiasing algorithm requires an adaptation gain that outpaces the perturbation decay. The uPT-ES replaces constant sinusoidal amplitudes with prescribed-time convergent functions and uses chirp signals with increasing frequency instead of stationary frequencies. This presentation also explores the application of uES to a source-seeking problem, where a ROS-based robot identifies a light source in a dark environment using real- time sensor data. Additionally, it examines the use of uES in maximum power point tracking (MPPT) for solar power systems to optimize the voltage across the solar array and its application under varying irradiance conditions in solar power setups.

Bio

Mamadou Diagne is an Associate Professor in the Department of Mechanical and Aerospace Engineering at the University of California, San Diego, affiliated with the Department of Electrical and Computer Engineering. He completed his Ph.D. in 2013 at the Laboratory of Control and Chemical Engineering at the University Claude Bernard Lyon I in Villeurbanne, France. Between 2017 and 2022, he was an Assistant Professor in the Department of Mechanical, Aerospace, and Nuclear Engineering at Rensselaer Polytechnic Institute in Troy, New York. From 2013 to 2016, he was a Postdoctoral Scholar, first at the University of California, San Diego, and then at the University of Michigan. His research focuses on controlling distributed parameter systems (DPS) and coupled PDEs and nonlinear ordinary differential equations, particularly on adaptive control, sampled-data control, and event- triggered control. Diagne has also coauthored influential studies on predictor feedback design for nonlinear systems with time-varying delays and extremum seeking. He serves as Associate Editor for Automatica and Systems and Control Letters. He is Vice-Chair for Industry of the IFAC Technical Committee on Adaptive and Learning Systems. He is a member of the Task Force on Diversity, Outreach, and Development Activities (DODA) of the IEEE Control System Society. He received the NSF Career Award in 2020.

References

Exponential and Prescribed-Time Extremum Seeking with Unbiased Convergence

https://acrobat.adobe.com/link/review?uri=urn:aaid:scds:US:ffd9a19d-c5f1-3c9c-9da8-dc55aefe00f1

Asymptotic, Exponential, and Prescribed-Time Unbiasing in Seeking of Time-Varying Extrema

https://acrobat.adobe.com/link/review?uri=urn:aaid:scds:US:7c827a2e-8191-3d52-aacd-9cf29d80c77b

Unbiased Extremum Seeking for PDEs

https://acrobat.adobe.com/link/review?uri=urn:aaid:scds:US:25d21656-2ef7-361e-8c4f-aa2c1e081783