Neural Networks Based Probability Density Function Control for Stochastic Systems

Sun, Xubin; Ding, Jun; Chai, Tianyou; Wang, Hong

doi:10.1007/978-1-84882-548-2_6

Cited by 3 publications

(8 citation statements)

References 7 publications

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“…With the development of image processing, several digital cameras can now be used to measure the distribution of the flame distribution, which can be further transferred into the temperature distribution. 63 An efficient combustion means that the distribution shape of temperature needs to be controlled. Because the distribution of flames directly relates the distribution of temperature, this can also be formulated to control the fuel flow rate so that the flame distribution (which can be represented as a multidimensional PDF) can be made to follow a target distribution that represents an efficient combustion.…”

Section: Flame Distribution Control Systems In Combustion Processesmentioning

confidence: 99%

“…The third application was made to the flame distribution control for a simple combustion system. 48,63 Moreover, discussions on the applications in chemical engineering have also been made. These applications have shown clearly the advantages of using SDC design in real-time control.…”

Section: Comparison With Traditional Stochastic Controlmentioning

confidence: 99%

“…In the earlier development of SDC, fixed‐basis functions were used as the reference set to approximate the instant output PDF. The use of neural networks for the output PDF control was the first group of approaches for generic SDC design, where neural networks were used to approximate the instant and measurable output PDFs and the neural network parameters (i.e., weights and biases) were dynamically linked to the control input 3,9,11,22,57,59,63,68,69,74 . In this regard, the following simple B‐spline neural network approximation was used in the initial developments of SDC to approximate the system output PDF at any time instant k :

γ false(y, u_{k} false) = \sum_{i = 1}^{n} w_{i} false(u_{k} false) B_{i} false(y false) + e false(y, u_{k} false); \forall y \in false[a, b false]

where

u_{k}

is the input at sample time,

k

w_{i} false(u_{k} false)

are the weights of the approximation to the output PDF, which is denoted by

γ false(y, u_{k} false)

B_{i} false(y false)

are the fixed‐basis functions, and

e false(y, u_{k} false)

is the approximation error.…”

Section: Sdc When Output Pdfs Are Measurablementioning

confidence: 99%

“…The use of neural networks for the output PDF control was the first group of approaches for generic SDC design, where neural networks were used to approximate the instant and measurable output PDFs and the neural network parameters (i.e., weights and biases) were dynamically linked to the control input. 3,9,11,22,57,59,63,68,69,74 In this regard, the following simple B-spline neural network approximation was used in the initial developments of SDC to approximate the system output PDF at any time instant k:…”

Section: Fixed-basis Function Approximationmentioning

confidence: 99%

“…The system produces a flame (or a temperature) distribution inside the combustion chamber. With the development of image processing, several digital cameras can now be used to measure the distribution of the flame distribution, which can be further transferred into the temperature distribution 63 . An efficient combustion means that the distribution shape of temperature needs to be controlled.…”

Section: Introductionmentioning

confidence: 99%

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Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Wang

2021

Optim Control Appl Methods

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Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

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Section: Flame Distribution Control Systems In Combustion Processesmentioning

confidence: 99%

Section: Comparison With Traditional Stochastic Controlmentioning

confidence: 99%

γ false(y, u_{k} false) = \sum_{i = 1}^{n} w_{i} false(u_{k} false) B_{i} false(y false) + e false(y, u_{k} false); \forall y \in false[a, b false]

where

u_{k}

is the input at sample time,

k

w_{i} false(u_{k} false)

are the weights of the approximation to the output PDF, which is denoted by

γ false(y, u_{k} false)

B_{i} false(y false)

are the fixed‐basis functions, and

e false(y, u_{k} false)

is the approximation error.…”

Section: Sdc When Output Pdfs Are Measurablementioning

confidence: 99%

Section: Fixed-basis Function Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Wang

2021

Optim Control Appl Methods

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Shaping of Molecular Weight Distribution Using Self-Optimizing Control Based on Moments

Su,

Zhou,

Tang

et al. 2024

Ind. Eng. Chem. Res.

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It is important but also challenging to control the full shape of the molecular weight distribution in polymerization processes, since it is an infinite dimensional probability density function (PDF). In this work, a self-optimizing control (SOC) strategy is adopted to achieve the aim of PDF shaping by maintaining some elaborately selected controlled variables (CVs) at constant set points through online feedback control, even in the presence of uncertainties. To find optimal CVs, finite moments rather than the full shape, which corresponds to an infinite-dimensional space, of the PDF are adopted as elements to parametrize CVs, while the optimization problem is to minimize the distance between the actual PDF and the target PDF. The proposed SOC-PDF method is demonstrated more effective than the existing stochastic distribution control method through a pilot semibatch styrene polymerization case study.

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Fault Tolerant Control of Fuzzy Stochastic Distribution Systems With Packet Dropout and Time Delay

Yao

2024

IEEE Trans. Automat. Sci. Eng.

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Neural Networks Based Probability Density Function Control for Stochastic Systems

Cited by 3 publications

References 7 publications

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Shaping of Molecular Weight Distribution Using Self-Optimizing Control Based on Moments

Fault Tolerant Control of Fuzzy Stochastic Distribution Systems With Packet Dropout and Time Delay

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