pith. sign in

arxiv: 2604.15922 · v1 · submitted 2026-04-17 · 📡 eess.SY · cs.SY

Uncertainty-based perturb and observe for data-driven optimization

Leontine Aarnoudse , Mark Haring , Nathan van de Wouw , Alexey Pavlov This is my paper

Pith reviewed 2026-05-10 07:58 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords perturb-and-observeuncertainty-based optimizationdata-driven optimizationtime-varying optimaphotovoltaic systemsadaptive optimizationconvergence
0
0 comments X

The pith

The paper presents an uncertainty-based perturb-and-observe method that reduces the number of perturbations needed for data-driven optimization of uncertain time-varying processes while ensuring convergence to the optimum.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Data-based adaptive optimization methods for uncertain and time-varying processes usually rely on continuous perturbation, which is often undesired in practice. The authors develop a new perturb-and-observe approach that uses estimates of uncertainty to trigger perturbations only when needed. This selective strategy is shown to converge to the optimum under mild conditions while still tracking changes in the optimum. A simulation case study on a photovoltaic solar array shows that the method requires fewer perturbations and outperforms the standard perturb-and-observe approach along with three other data-based methods.

Core claim

The uncertainty-based perturb-and-observe method, grounded in the principle of only perturbing when needed, converges to the optimum for time-varying processes under mild conditions while requiring significantly fewer perturbations than continuous perturbation approaches.

What carries the argument

The uncertainty estimate that decides whether a perturbation step is performed at each iteration of the data-driven optimization loop.

If this is right

  • The number of perturbations required for optimization is reduced compared to continuous perturbation methods.
  • The algorithm retains the ability to track time-varying optima.
  • Convergence holds under mild conditions that are stated for the method.
  • Superior performance appears in the photovoltaic solar array simulation relative to standard perturb-and-observe and other data-based methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The selective perturbation rule could lower intervention costs in other industrial or autonomous systems where frequent adjustments are expensive.
  • Replacing the uncertainty estimator with more sophisticated probabilistic models might tighten the conditions needed for reliable decisions.
  • If uncertainty estimates degrade in the presence of unmodeled disturbances, the method risks either over-perturbing or losing track of the optimum.
  • Hardware experiments with sensor noise and actuator limits would provide a direct test of the simulation advantages.

Load-bearing premise

The method depends on obtaining sufficiently accurate uncertainty estimates and on the mild conditions for convergence holding in the target process.

What would settle it

A controlled simulation or experiment on a process with known time-varying optimum in which the uncertainty estimates are made deliberately inaccurate, resulting in either divergence or no net reduction in perturbations compared to standard methods.

Figures

Figures reproduced from arXiv: 2604.15922 by Alexey Pavlov, Leontine Aarnoudse, Mark Haring, Nathan van de Wouw.

Figure 1
Figure 1. Figure 1: Example of the weights ωj,k as a function of j for λ = e −0.5 , k = 2 and M = 0 ( ), M = 1 ( ), M = 2 ( ), M = 3 ( ) and M = 4 ( ). about the current function value than newer measurements. This is done to take into account any time-variations of the function without explicitly modeling those. The weights should be close to 1 for small values of k − j (recent measurements), and reduce to 0 for increasing v… view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the decision process of uncertainty [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: In the simulation example, function fk(u) is the steady-state produced power P of a photovoltaic array as a function of the duty cycle u, shown at time indices k = 50 ( ), k = 150 ( ) and k = 250 ( ). The squares indicate the possible inputs. TABLE I: Parameters for the photovoltaic model. Parameter Description Tr = 298.15 K Reference temperature Is = 5.61 A Reference short-circuit current at Tr I0 = 1.13 … view at source ↗
Figure 4
Figure 4. Figure 4: Temperature ( ) and solar irradiance ( ) between 6AM (k = 0) and 6PM (k = 300) on a clear and sunny day. light-generated current is and the reverse saturation current i0 are given by is = (Is + ki(T − Tr)) S 1000 (48) i0 = I0  T Tr 3 e Eg NVt ( T Tr −1) , Vt = kT q , (49) for a photovoltaic cell with temperature T and solar irra￾diance S. All parameters are given in Table I. The output current i of an ar… view at source ↗
Figure 6
Figure 6. Figure 6: Using uncertainty-based P&O ( ) leads to a 2.5% increase in total power output over a day compared to standard P&O ( ). The uP&O output is 7.8% higher than the maximum power output using a constant duty cycle ( ), and only 1.8% lower than the maximum output if the optimal duty cycle is always known exactly ( ). tracking the duty cycle that maximizes the energy output for the solar array. For uP&O, the para… view at source ↗
Figure 7
Figure 7. Figure 7: The presented uncertainty-based P&O method ( [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

Data-based adaptive optimization methods hold great promise for the performance optimization of uncertain, time-varying processes. However, current methods are often based on continuous perturbation which is in general undesired for real-life (e.g., industrial) applications. In this paper, a new uncertainty-based perturb-and-observe method is developed that addresses this limitation and reduces the required number of perturbations, while retaining the capability to track time-varying optima. The method is based on the philosophy of `only perturbing when needed,' and is shown to converge to the optimum under mild conditions. A simulation-based case study on a photo-voltaic solar array demonstrates that it can outperform the standard perturb and observe approach as well as three other data-based optimization methods.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes an uncertainty-based perturb-and-observe (P&O) method for data-driven optimization of uncertain, time-varying processes. It reduces the number of perturbations via an 'only perturb when needed' rule based on uncertainty estimates, claims convergence to the optimum under mild conditions while retaining tracking capability for drifting optima, and reports outperformance versus standard P&O and three other data-based methods in a photovoltaic solar-array simulation.

Significance. If the convergence result holds under verifiable mild conditions and the method generalizes, it would represent a practical advance for industrial applications where continuous perturbation is costly or disruptive, by lowering intervention frequency without sacrificing adaptability. The PV simulation provides initial empirical support for efficiency gains, but the absence of detailed derivation and error analysis limits immediate impact.

major comments (2)
  1. [Abstract / Convergence Analysis] Abstract and convergence section: the central claim that the method 'is shown to converge to the optimum under mild conditions' lacks the precise statement of those conditions, the theorem statement, and the key derivation steps (e.g., construction of the uncertainty set, formalization of the perturbation decision rule, and handling of online updates for time-varying optima). This is load-bearing for the main theoretical contribution.
  2. [Case Study / Simulation Results] Simulation section: the reported outperformance depends on unspecified details of uncertainty estimation, tuning, and data handling; without these, the PV results cannot serve as independent verification of the general claim and risk being sensitive to implementation choices.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it briefly indicated the form of uncertainty quantification employed (e.g., set-membership, probabilistic).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the opportunity to clarify and strengthen the manuscript. We address each major comment below and will incorporate revisions to improve the presentation of the theoretical results and the reproducibility of the simulations.

read point-by-point responses

  1. Referee: [Abstract / Convergence Analysis] Abstract and convergence section: the central claim that the method 'is shown to converge to the optimum under mild conditions' lacks the precise statement of those conditions, the theorem statement, and the key derivation steps (e.g., construction of the uncertainty set, formalization of the perturbation decision rule, and handling of online updates for time-varying optima). This is load-bearing for the main theoretical contribution.

    Authors: We agree that the convergence claim requires a more explicit and self-contained presentation to be fully verifiable. While the manuscript develops the uncertainty-based decision rule and sketches the convergence argument under assumptions such as bounded uncertainty estimates and Lipschitz continuity of the underlying objective, the formal theorem statement and key derivation steps are not stated with sufficient precision in the abstract or main convergence section. In the revised manuscript we will insert a clearly labeled theorem that enumerates the mild conditions (including the construction of the data-driven uncertainty set, the threshold-based perturbation rule, and the mechanism for online adaptation to drifting optima), followed by an outline of the principal proof steps. This change will make the theoretical contribution load-bearing and easier to check without altering the underlying analysis. revision: yes

  2. Referee: [Case Study / Simulation Results] Simulation section: the reported outperformance depends on unspecified details of uncertainty estimation, tuning, and data handling; without these, the PV results cannot serve as independent verification of the general claim and risk being sensitive to implementation choices.

    Authors: We acknowledge that the simulation results, while supportive, cannot be independently verified without additional implementation specifics. The current manuscript describes the photovoltaic array model and comparative metrics but leaves the precise uncertainty estimator (e.g., the regression technique and variance computation), tuning parameters (perturbation amplitude and uncertainty threshold), and data-handling protocol (online data window and update frequency) only partially specified. In the revision we will expand the simulation section with these details, including a table of all numerical parameters and, if space permits, pseudocode for the uncertainty estimation and decision rule. This will allow readers to reproduce the reported gains and assess sensitivity to implementation choices. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation and convergence claim are independent of fitted inputs or self-referential definitions

full rationale

The paper introduces an uncertainty-based perturb-and-observe algorithm grounded in the explicit philosophy of 'only perturbing when needed.' The central result is a convergence statement under stated mild conditions, supported by a PV-array simulation case study that compares performance against standard P&O and other data-driven methods. No equations or steps reduce a claimed prediction to a fitted parameter by construction, no uniqueness theorem is imported from self-citation to force the method, and the uncertainty set construction is presented as a design choice rather than a tautology. The derivation chain therefore remains self-contained against external benchmarks and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No specific free parameters, axioms, or invented entities can be identified from the abstract alone.

pith-pipeline@v0.9.0 · 5424 in / 1076 out tokens · 31171 ms · 2026-05-10T07:58:54.220272+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

  1. [1]

    Modified perturb and observe MPPT algorithm for drift avoidance in photovoltaic systems,

    M. Killi and S. Samanta, “Modified perturb and observe MPPT algorithm for drift avoidance in photovoltaic systems,”IEEE Trans. Ind. Electron., vol. 62, no. 9, pp. 5549–5559, 2015

    work page 2015

  2. [2]

    A real-time cost optimization of two-section oven system with discrete gradient extremum seeking control: An experimental study in iron and steel industry,

    S. Yilmaz and M. Furat, “A real-time cost optimization of two-section oven system with discrete gradient extremum seeking control: An experimental study in iron and steel industry,”J. Process Control, vol. 122, pp. 84–99, 2023

    work page 2023

  3. [3]

    Robust Extremum Seeking Control with application to Gas Lifted Oil Wells,

    D. Krishnamoorthy, A. Pavlov, and Q. Li, “Robust Extremum Seeking Control with application to Gas Lifted Oil Wells,”IFAC- PapersOnLine, vol. 49, no. 13, pp. 205–210, 2016

    work page 2016

  4. [4]

    Extremum seeking control applied to operation of dividing wall column – DWC,

    I. J. Halvorsen, L. I. M. Aarnoudse, M. A. M. Haring, and S. Skoges- tad, “Extremum seeking control applied to operation of dividing wall column – DWC,”Syst. Control Trans., vol. 4, pp. 1157–1162, 2025

    work page 2025

  5. [5]

    Stability of extremum seeking feedback for general nonlinear dynamic systems,

    M. Krsti ´c and H.-H. Wang, “Stability of extremum seeking feedback for general nonlinear dynamic systems,”Automatica, vol. 36, no. 4, pp. 595–601, 2000

    work page 2000

  6. [6]

    100 years of extremum seeking: A survey,

    A. Scheinker, “100 years of extremum seeking: A survey,”Automatica, vol. 161, p. 111481, 2024

    work page 2024

  7. [7]

    Extremum Control Systems - An Area for Adaptive Control?

    J. Sternby, “Extremum Control Systems - An Area for Adaptive Control?” inJt. Autom. Control Conf., 1980, pp. W A2–A

    work page 1980

  8. [8]

    Maximum photovoltaic power tracking: an algorithm for rapidly changing atmo- spheric conditions,

    K. H. Hussein, I. Muta, T. Hoshino, and M. Osakada, “Maximum photovoltaic power tracking: an algorithm for rapidly changing atmo- spheric conditions,”IEE Proc. Gener. Transm. Distrib., vol. 142, no. 1, pp. 59–64, 1995

    work page 1995

  9. [9]

    Altitude Optimization of Airborne Wind Energy Systems via Switched Extremum Seeking-Design, Anal- ysis, and Economic Assessment,

    A. Bafandeh and C. Vermillion, “Altitude Optimization of Airborne Wind Energy Systems via Switched Extremum Seeking-Design, Anal- ysis, and Economic Assessment,”IEEE Trans. Control Syst. Technol., vol. 25, no. 6, pp. 2022–2033, 2017

    work page 2022

  10. [10]

    Extremum Seeking Control for optimization of a feed-forward Pelton turbine speed controller in a fixed-displacement hydraulic wind turbine concept,

    S. Mulders, N. Diepeveen, and J. van Wingerden, “Extremum Seeking Control for optimization of a feed-forward Pelton turbine speed controller in a fixed-displacement hydraulic wind turbine concept,” J. Phys. Conf. Ser., vol. 1222, no. 1, p. 012015, may 2019

    work page 2019

  11. [11]

    Optimization of Perturb and Observe Maximum Power Point Tracking Method,

    N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of Perturb and Observe Maximum Power Point Tracking Method,”IEEE Trans. Power Electron., vol. 20, no. 4, pp. 963–973, jul 2005

    work page 2005

  12. [12]

    Micro-Testing While Drilling for Rate of Penetration Optimization: Experiments and Sim- ulations,

    M. Nystad, B. S. Aadnøy, and A. Pavlov, “Micro-Testing While Drilling for Rate of Penetration Optimization: Experiments and Sim- ulations,”J. Offshore Mech. Arct. Eng., vol. 144, no. 3, p. 031801, 2022

    work page 2022

  13. [13]

    Extremum Seeking With Enhanced Convergence Speed for Opti- mization of Time-Varying Steady-State Behavior of Industrial Motion Stages,

    L. Hazeleger, J. van de Wijdeven, M. Haring, and N. van de Wouw, “Extremum Seeking With Enhanced Convergence Speed for Opti- mization of Time-Varying Steady-State Behavior of Industrial Motion Stages,”IEEE Trans. Control Syst. Technol., vol. 30, no. 2, pp. 464– 480, 2022

    work page 2022

  14. [14]

    On non-local stability properties of extremum seeking control,

    Y . Tan, D. Nesic, and I. Mareels, “On non-local stability properties of extremum seeking control,”Automatica, vol. 42, pp. 889–903, 2006

    work page 2006

  15. [15]

    Extremum-seeking control for nonlinear systems with periodic steady-state outputs,

    M. Haring, N. van de Wouw, and D. Neˇsi´c, “Extremum-seeking control for nonlinear systems with periodic steady-state outputs,”Automatica, vol. 49, no. 6, pp. 1883–1891, 2013

    work page 2013

  16. [16]

    Multivariable Newton-based extremum seeking,

    A. Ghaffari, M. Krsti ´c, and D. Ne ˇsi´c, “Multivariable Newton-based extremum seeking,”Automatica, vol. 48, no. 8, pp. 1759–1767, 2012

    work page 2012

  17. [17]

    Fast extremum seeking using multisine dither and online complex curve fitting,

    T. van Keulen, R. van der Weijst, and T. Oomen, “Fast extremum seeking using multisine dither and online complex curve fitting,”IFAC Pap., vol. 53, no. 2, pp. 5362–5367, 2020

    work page 2020

  18. [18]

    Data-efficient extremum-seeking control using kernel-based function,

    W. Weekers, A. Saccon, and N. van de Wouw, “Data-efficient extremum-seeking control using kernel-based function,”Automatica, vol. 181, p. 112506, 2025

    work page 2025

  19. [19]

    Automatic crossbow control in industrial hot-dip galvanizing lines,

    L. Marko, A. Kugi, and A. Steinboeck, “Automatic crossbow control in industrial hot-dip galvanizing lines,”J. Process Control, vol. 122, pp. 147–158, 2023

    work page 2023

  20. [20]

    A comparative study of an exponential adaptive perturb and observe algorithm and ripple correlation control for real-time optimization,

    V . T. Buyukdegirmenci, A. M. Bazzi, and P. T. Krein, “A comparative study of an exponential adaptive perturb and observe algorithm and ripple correlation control for real-time optimization,”IEEE 12th Work. Control Model. Power Electron., 2010

    work page 2010

  21. [21]

    Phasor ex- tremum seeking control with adaptive perturbation amplitude,

    K. T. Atta, R. Hostettler, W. Birk, and A. Johansson, “Phasor ex- tremum seeking control with adaptive perturbation amplitude,” inIEEE 55th Conf. Decis. Control, 2016, pp. 7069–7074

    work page 2016

  22. [22]

    Lyapunov-based switched extremum seeking for photovoltaic power maximization,

    S. J. Moura and Y . A. Chang, “Lyapunov-based switched extremum seeking for photovoltaic power maximization,”Control Eng. Pract., vol. 21, no. 7, pp. 971–980, 2013

    work page 2013

  23. [23]

    Predictive & Adaptive MPPT Perturb and Observe Method,

    N. Femia, D. Granozio, G. Petrone, G. Spagnuolo, and M. Vitelli, “Predictive & Adaptive MPPT Perturb and Observe Method,”IEEE Trans. Aerosp. Electron. Syst., vol. 43, no. 3, pp. 934–950, 2007

    work page 2007

  24. [24]

    A mod- ified MPPT method with variable perturbation step for photovoltaic system,

    Chao Zhang, Dean Zhao, Jinjing Wang, and Guichang Chen, “A mod- ified MPPT method with variable perturbation step for photovoltaic system,” in2009 IEEE 6th Int. Power Electron. Motion Control Conf., vol. 3. IEEE, may 2009, pp. 2096–2099

    work page 2009

  25. [25]

    Uncertainty-Based Perturb and Observe for Fast Optimization of Unknown, Time-Varying Processes *,

    L. Aarnoudse, M. Haring, N. van de Wouw, and A. Pavlov, “Uncertainty-Based Perturb and Observe for Fast Optimization of Unknown, Time-Varying Processes *,” in2025 IEEE 64th Conf. Decis. Control. IEEE, 2025, pp. 2268–2273

    work page 2025

  26. [26]

    Efficient Global Optimization of Expensive Black-Box Functions,

    D. R. Jones, M. Schonlau, and J. Welch, William, “Efficient Global Optimization of Expensive Black-Box Functions,”J. Glob. Optim., vol. 13, pp. 455–492, 1998

    work page 1998

  27. [27]

    On the Likelihood that One Unknown Proba- bility Exceeds Another in View of the Evidence of Two Samples,

    W. R. Thompson, “On the Likelihood that One Unknown Proba- bility Exceeds Another in View of the Evidence of Two Samples,” Biometrika, vol. 25, no. 3/4, pp. 285–294, 1933

    work page 1933

  28. [28]

    An Empirical Evaluation of Thompson Sampling,

    O. Chapelle and L. Li, “An Empirical Evaluation of Thompson Sampling,” inAdv. Neural Inf. Process. Syst., 2011

    work page 2011

  29. [29]

    A Hybrid Photovoltaic Simulator for Utility Interactive Studies,

    G. Vachtsevanos and K. Kalaitzakis, “A Hybrid Photovoltaic Simulator for Utility Interactive Studies,”IEEE Trans. Energy Convers., vol. EC- 2, no. 2, pp. 227–231, 1987

    work page 1987

  30. [30]

    Detection of Internal Resistance Change for Photovoltaic Arrays Using Extremum-Seeking Control MPPT Signals,

    X. Li, Y . Li, J. E. Seem, and P. Lei, “Detection of Internal Resistance Change for Photovoltaic Arrays Using Extremum-Seeking Control MPPT Signals,”IEEE Trans. Control Syst. Technol., vol. 24, no. 1, pp. 325–333, 2016

    work page 2016