Extremum seeking control with attenuated steady-state oscillations

Bhattacharjee, Diganta; Subbarao, Kamesh

doi:10.1016/j.automatica.2020.109432

Cited by 19 publications

(9 citation statements)

References 29 publications

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“…The secondary goal cannot be accomplished by techniques that diminish the oscillation amplitude over time (Abdelgalil & Taha, 2021;Bhattacharjee & Subbarao, 2021) as the cost functions are slowly-varying and the learning procedure would stop prematurely. Furthermore, we cannot use too high frequencies (Suttner, 2019) as that would also destroy our equipment.…”

Section: Perturbation Signal Optimization In Oil Extractionmentioning

confidence: 99%

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

Krilašević

Grammatico

2023

Automatica

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Section: Perturbation Signal Optimization In Oil Extractionmentioning

confidence: 99%

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

Krilašević

Grammatico

2023

Automatica

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“…Then, in this order, for the terms appearing in (41) we use the definition of the Lipschitz constant of h(•), (27) , the Mean Value Theorem, and (39) to obtain…”

Section: Appendix IV Proof Of Theoremmentioning

confidence: 99%

“…So, to overcome this issue, the dither amplitude should be sufficiently large to make the estimation of the cost variation robust in respect of local cost fluctuations [25]. For this reason, some authors suggested an adaptation policy for the dither amplitude which shrinks δ over time so that at the beginning a large dither lets the ES overcome local minima while asymptotically a small dither guarantees good optimisation performances [26], [27].…”

Section: Introductionmentioning

confidence: 99%

“…(53)Now, since ∂ε δ (x, ȳ, t)/∂x = ∂y δ (x)/∂x and (5) coincides with (14a), we can exploit(36) to bound∂ε δ (x, ȳa , t) − b 1,δ (x)/2 ∂x x=xa ≤ 2L r . (54)Then, substitute (54) into (53) and use(27) and (39) to bound∂ǫ 1 (η, t) ∂η η=ηa ηa ≤ γδL 2 r 3(55)and use (42), (51), (52) and (55) to bound (48) as|x(t) − z 1 (t)| ≤ |x(0) − z 1 (0)| + tγ 2 k3 (L r , δ) + r |x(τ ) − z 1 (τ )| + |ȳ(τ ) − z 2 (τ )|dτ(56)where k1 (L r , δ) := δL r (2 + L r (3 + L r ) + 3L r ). We now use the same conceptual steps (46)-(56) to find a bound for|ȳ(τ ) − z 2 (τ )|.…”

mentioning

confidence: 99%

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Uniform non-convex optimisation via Extremum Seeking

Mimmo¹,

Marconi²,

Notarstefano³

2022

Preprint

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The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the global minimiser to be semi-global practically stable despite the presence of local minima. Under the assumption of a globally Lipschitz cost function, it is shown that the scheme, improved through a high-pass filter, makes the global minimiser practically stable with a global domain of attraction.

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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.…”

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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Extremum seeking control with attenuated steady-state oscillations

Cited by 19 publications

References 29 publications

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

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

Uniform non-convex optimisation via Extremum Seeking

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

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