Extremum seeking control with an adaptive dither signal

Suttner, Raik

doi:10.1016/j.automatica.2018.11.055

Cited by 29 publications

(20 citation statements)

References 29 publications

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“…The shape affects the convergence rate of the gradient estimator [6]. Dither signal frequency should be sufficiently high in relation to the dynamics in the gradient estimator, process optimizer and the plant dynamics to guarantee convergence to the optimum through time scales separation between these dynamics [3], [15]. The amplitude should be chosen sufficiently small to be able to extract the essentially local information on the gradient of the cost function.…”

Section: Introductionmentioning

confidence: 99%

Dither signal optimization for multi-agent extremum seeking control

Silva

Pavlov

2020

2020 European Control Conference (ECC)

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In this paper we formulate and solve the problem of multi-agent extremum seeking with dither signals optimization. The solution is a distributed perturbation-based extremum-seeking controller with an additional objective of minimizing overall dither signals disturbances for the whole system. In particular, the proposed method dynamically calculates dither signals for individual subsystems to minimize the dither-induced variations in the total input and output of the process. The overall scheme consists of a dither signal optimizer coupled with a least-squares gradient estimator and a distributed synchronization-based process optimizer. Simulation results for an oil production system with multiple gas-lifted wells demonstrate that the proposed controller is capable of optimizing the production process, while minimizing, on the fast time scale, dither-induced variations both in the total input (total gas injection rate) and in the total output (total oil production rate) of the production system.

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Section: Introductionmentioning

confidence: 99%

Dither signal optimization for multi-agent extremum seeking control

Silva

Pavlov

2020

2020 European Control Conference (ECC)

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“…The secondary goal cannot be accomplished by techniques that diminish the oscillation amplitude over time [1], [3] as the cost functions are slowly-varying and the learning procedure would stop prematurely. Furthermore, we cannot use too high frequencies [45] as that would also destroy our equipment. Thus, to accomplish our goal, wells are grouped into pairs (i, j), and each pair selects perturbation signals which are in antiphase:…”

Section: Perturbation Signal Optimization In Oil Extractionmentioning

confidence: 99%

Learning generalized Nash equilibria in monotone games: A hybrid adaptive extremum seeking control approach

Krilašević¹,

Grammatico²

2021

Preprint

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In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information to compute a GNE with a central coordinator. As the second main contribution, we design a gain adaptation scheme for the previous algorithm in order to alleviate the problem of improper scaling of the cost functions versus the constraints. Third, we propose a data-driven variant of the former algorithm, where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values. Finally, we apply our method to a perturbation amplitude optimization problem in oil extraction engineering.

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“…In this section, we demonstrate our esc controller for the 2 state benchmark example from [20]. The plant dynamics are…”

Section: -D Benchmarkmentioning

confidence: 99%

“…In contrast, this paper focuses on accelerating convergence by using an adaptive step-size in the integral-action of the gradient descent. While dither perturbation has gained widespread attention, directly adapting the esc controller gain is relatively uncommon, with a few exceptions, namely [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error

Danielson¹,

Bortoff²,

Chakrabarty³

2021

Preprint

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This paper presents an extremum-seeking control (esc) algorithm with an adaptive step-size that adjusts the aggressiveness of the controller based on the quality of the gradient estimate. The adaptive step-size ensures that the integral-action produced by the gradient descent does not destabilize the closedloop system. To quantify the quality of the gradient estimate, we present a batch least-squares (bls) estimator with a novel weighting and show that it produces bounded estimation errors, where the uncertainty is due to the curvature of the unknown cost function. The adaptive step-size then maximizes the decrease of the combined plant and controller Lyapunov function for the worst-case estimation error. We prove that our esc controller is input-to-state stable with respect to the dither signal. Finally, we demonstrate our esc controller through five numerical examples; one illustrative, one practical, and three benchmarks.

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Extremum seeking control with an adaptive dither signal

Cited by 29 publications

References 29 publications

Dither signal optimization for multi-agent extremum seeking control

Dither signal optimization for multi-agent extremum seeking control

Learning generalized Nash equilibria in monotone games: A hybrid adaptive extremum seeking control approach

Extremum Seeking Control with an Adaptive Gain Based On Gradient Estimation Error

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