Unbiased Extremum Seeking: Applications to Source Seeking and Solar Power Systems

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 ?rst 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 identi?es 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.

Speaker: Mamadou Diagne, UC San Diego