Computational aspects of Kolmogorov's superposition theorem

Katsuura, Hidefumi; Sprecher, David A.

doi:10.1016/0893-6080(94)90079-5

Cited by 42 publications

(18 citation statements)

References 5 publications

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“…In fact, Kurkova [9] uses the Kolmogorov Superposition Theorem to construct approximations in the two hidden layer MLP model with an arbitrary sigmoidal function, where the number of units needed is dependent on the smoothness properties of the function approximated and the desired error of approximation (this number grows to in"nity as the error decreases). Kurkova [9] and others (see [3,7,16,17,20]) are interested in using the Kolmogorov Superposition Theorem to "nd good algorithms for approximation. This is not our aim.…”

Section: Two Hidden Layersmentioning

confidence: 99%

Lower bounds for approximation by MLP neural networks

1999

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Section: Two Hidden Layersmentioning

confidence: 99%

Lower bounds for approximation by MLP neural networks

1999

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“…(Also an estimate of the number of hidden units was provided in [41] and [42].) For further work on the computational aspects of the Kolmogorov Superposition Theorem and its connections with neural networks, we refer the reader to [43] and [44]. An innovative neural-network architecture based on this theorem was later proposed in [45].…”

Section: A Bunch Of Seminal Papersmentioning

confidence: 99%

Universal Approximation by Ridge Computational Models and Neural Networks: A Survey

Sanguineti

2008

TOAMJ

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“…For MISO transfer function system, the superposition theorem can be used for analysis, namely one disturbance at a time is considered [20]. It is considered that the disturbance of the wind speed is set to zero when analyzing the impact of the load disturbance on the system frequency.…”

Section: Extended Sfr Modelmentioning

confidence: 99%

An Extended System Frequency Response Model Considering Wind Power Participation in Frequency Regulation

et al. 2017

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With increasing penetration of wind power into the power system, wind power participation in frequency regulation is regarded as a beneficial strategy to improve the dynamic frequency response characteristics of power systems. The traditional power system frequency response (SFR) model, which only includes synchronous generators, is no longer suitable for power systems with high penetrated wind power. An extended SFR model, based on the reduced-order model of wind turbine generator (WTG) and the traditional SFR model, is presented in this paper.In the extended SFR model, the reduced-order model of WTG with combined frequency control is deduced by employing small signal analysis theory. Afterwards, the stability analysis of a closed-loop control system for the extended SFR model is carried out. Time-domain simulations using a test system are performed to validate the effectiveness of the extended SFR model; this model can provide a simpler, clearer and faster way to analyze the dynamic frequency response characteristic for a high-wind integrated power systems. The impact of additional frequency control parameters and wind speed disturbances on the system dynamic frequency response characteristics are investigated.

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Computational aspects of Kolmogorov's superposition theorem

Cited by 42 publications

References 5 publications

Lower bounds for approximation by MLP neural networks

Lower bounds for approximation by MLP neural networks

Universal Approximation by Ridge Computational Models and Neural Networks: A Survey

An Extended System Frequency Response Model Considering Wind Power Participation in Frequency Regulation

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