arXiv subjects

Cemal Tugrul Yilmaz

Publications and source records attributed to Cemal Tugrul Yilmaz.

5 recordsLinked to original sources

arXiv2025

Unbiased Extremum Seeking for MPPT in Photovoltaic Systems

This paper presents novel extremum seeking (ES) strategies for maximum power point tracking (MPPT) in photovoltaic (PV) systems that ensure unbiased convergence and prescribed-time performance. Conventional ES methods suffer from steady-state bias due to persistent dither signal. We introduce two novel ES algorithms: the exponential unbiased ES (uES), which guarantees exponential convergence to the maximum power point (MPP) without steady-state oscillation bias, and the unbiased prescribed-time ES (uPT-ES), which ensures convergence within a user-defined time horizon. Both methods leverage time-varying perturbation amplitudes and demodulation gains, with uPT-ES additionally utilizing chirp signals to enhance excitation over finite-time intervals. Experimental results on a hardware-in-the-loop testbed validate the proposed algorithms, demonstrating improved convergence speed and tracking accuracy compared to classical ES, under both static and time-varying environmental conditions.

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arXiv2024

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

Our recently developed "unbiased" extremum seeking (uES) algorithms ensure perfect convergence to the optimum at a user-assigned exponential rate or, more powerfully, within a user-prescribed time. Unlike classical approach, these algorithms use time-varying adaptation and controller gains, along with constant or time-varying probing frequencies (chirp signals). This paper advances our earlier uES designs from strongly convex maps with static optima to a broader class of convex cost functions with time-varying optima diverging at arbitrary rates, even in finite time. This advancement first motivates the use of Lie bracket averaging instead of classical averaging due to the average system system, which doesn't necessarily need to be exponentially convergent, and the existence of non-periodic time-varying parameters; second, it necessitates the formulation of non-trivial and key feasibility conditions for the choice of time-varying design parameters and their decay/growth rates in relation to the convexity of the map and the divergence rate of optima. These conditions indicate that, for constant-frequency probing, the user-defined asymptotic rate of unbiasing is limited by the convexity of the map. However, this rate can be made arbitrarily fast (including asymptotic, exponential, and prescribed time) using chirpy probing, which requires sufficiently rapid frequency and adaptation growth to enable tracking of faster-diverging optima. In addition to numerical simulations of the designs, we experimentally test the feasibility of exponential uES for tuning the angular velocity of a unicycle to seek a static light source.

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arXiv2024

Unbiased Extremum Seeking for PDEs

There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics. In contrast to prior PDE-compensating ES designs, which only guarantee local stability around the extremum, we introduce unbiased ES that compensates for delay and diffusion PDE dynamics while ensuring exponential and unbiased convergence to the optimum. Our method leverages exponentially decaying/growing signals within the modulation/demodulation stages and carefully selected design parameters. The stability analysis of our designs relies on a state transformation, infinite-dimensional averaging, local exponential stability of the averaged system, local stability of the transformed system, and local exponential stability of the original system. Numerical simulations are presented to demonstrate the efficacy of the developed designs.

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arXiv2024

Perfect Tracking of Time-Varying Optimum by Extremum Seeking

This paper introduces extremum seeking (ES) algorithms designed to achieve perfect tracking of arbitrary time-varying extremum. In contrast to classical ES approaches that employ constant frequencies and controller gains, our algorithms leverage time-varying parameters, growing either asymptotically or exponentially, to achieve desired convergence behaviors. Our stability analysis involves state transformation, time-dilation transformation, and Lie bracket averaging. The state transformation is based on the multiplication of the input state by asymptotic or exponential growth functions. The time transformation enables tracking of the extremum as it gradually converges to a constant value when viewed in the dilated time domain. Finally, Lie bracket averaging is applied to the transformed system, ensuring practical uniform stability in the dilated time domain as well as asymptotic or exponential stability of the original system in the original time domain. We validate the feasibility of these designs through numerical simulations.

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arXiv2023

Exponential and Prescribed-Time Extremum Seeking with Unbiased Convergence

We present multivariable extremum seeking (ES) designs that achieve unbiased convergence to the optimum. Two designs are introduced: one with exponential unbiased convergence (unbiased extremum seeker, uES) and the other with user-assignable prescribed-time unbiased convergence (unbiased PT extremum seeker, uPT-ES). In contrast to the conventional ES, which uses persistent sinusoids and results in steady-state oscillations around the optimum, the exponential uES employs an exponentially decaying amplitude in the perturbation signal (for achieving convergence) and an exponentially growing demodulation signal (for making the convergence unbiased). The achievement of unbiased convergence also entails employing an adaptation gain that is sufficiently large in relation to the decay rate of the perturbation amplitude. Stated concisely, the bias is eliminated by having the learning process outpace the waning of the perturbation. The other algorithm, uPT-ES, employs prescribed-time convergent/blow-up functions in place of constant amplitudes of sinusoids, and it also replaces constant-frequency sinusoids with chirp signals whose frequency grows over time. Among the convergence results in the ES literature, uPT-ES may be the strongest yet in terms of the convergence rate (prescribed-time) and accuracy (unbiased). To enhance the robustness of uES to a time-varying optimum, exponential functions are modified to keep oscillations at steady state. Stability analysis of the designs is based on a state transformation, averaging, local exponential/PT stability of the averaged system, local stability of the transformed system, and local exponential/PT stability of the original system. For numerical implementation of the developed ES schemes and comparison with previous ES designs, the problem of source seeking by a two-dimensional velocity-actuated point mass is considered.

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