Volterra integral equations: An approach based on Lipschitz-continuity

Martire, Antonio Luciano

doi:10.1016/j.amc.2022.127496

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…(2) For all t ∈ {0, 1, • • • T} and k = 0, 1, 2, • • • , when ∆u i k (t) = 0, the system of Equation (1) satisfies generalized Lipschitz continuity [35], that is, ∀t ∈ {0,…”

Section: Nonparametric Adaptive Iterative Control Of Vertical Quenchi...mentioning

confidence: 99%

Multi-Zone Integrated Iterative-Decoupling Control of Temperature Field of Large-Scale Vertical Quenching Furnaces Based on ESRNN

Shen

Chen

2023

Processes

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Temperature uniformity within a large vertical quenching furnace is the key factor to determine the properties of aluminum workpieces. The existing temperature control method for quenching furnaces cannot overcome the influence of multi-zone coupling issues, which lead to unstable product performance and a lack of key performance. Based on a workpiece temperature field model, a spatial-temporal dimensional extrapolation method is proposed to realize fast and accurate solving of the temperature model. In view of the over-burning and under-burning problems during the temperature rising period, a self-incentive nonparametric adaptive iterative control algorithm is presented, which realizes consistent temperature rising of multiple heating zones. Aiming at the strong coupling problem of the multi-zone heating manner during the temperature holding period, the decoupling problem of multiple control loops is converted into a multi-loop integrated control optimization problem. An eigenvector self-update recurrent neural network (ESRNN) is constructed to determine the Jacobian information and tune the control parameters of each loop controller in real time, thereby realizing the integrated intelligent decoupling control of multiple heating loops. Simulation and industrial results verify the superiority of the proposed method, which can realize high-precision and high-uniformity control of a large-scale temperature field and effectively improve the quality and performance of aluminum alloy workpieces.

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Section: Nonparametric Adaptive Iterative Control Of Vertical Quenchi...mentioning

confidence: 99%

Multi-Zone Integrated Iterative-Decoupling Control of Temperature Field of Large-Scale Vertical Quenching Furnaces Based on ESRNN

Shen

Chen

2023

Processes

View full text Add to dashboard Cite

show abstract

“…RM120172B84AD5EC. 2 Corresponding author probability, [10]. Different classifications of integral equations exist, depending on the suitable analytical properties: we distinguish between Fredholm and Volterra integral equations of first and second kind, depending on whether the unknown function appears only under the integral sign or not.…”

Section: Introductionmentioning

confidence: 99%