A fully probabilistic control framework for stochastic systems with input and state delay

Herzallah, Randa; Zhou, Yuqiu

doi:10.1038/s41598-022-11514-z

Cited by 5 publications

(7 citation statements)

References 37 publications

(58 reference statements)

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“…In practical applications, a wide array of engineering and control systems, ranging from aircraft and robots to power systems, exhibit stochastic characteristics [20][21][22]. A description of a stochastic system can be expressed as follows:…”

Section: System Statementmentioning

confidence: 99%

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

Liu,

Zhang,

Zhou

et al. 2024

Mathematics

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This study presents a novel event-triggered relearning framework for neural network modeling, designed to improve prediction precision in dynamic stochastic complex industrial systems under non-stationary and variable conditions. Firstly, a sliding window algorithm combined with entropy is applied to divide the input and output datasets across different operational conditions, establishing clear data boundaries. Following this, the prediction errors derived from the neural network under different operational states are harnessed to define a set of event-triggered relearning criteria. Once these conditions are triggered, the relevant dataset is used to recalibrate the model to the specific operational condition and predict the data under this operating condition. When the predicted data fall within the training input range of a pre-trained model, we switch to that model for immediate prediction. Compared with the conventional BP neural network model and random vector functional-link network, the proposed model can produce a better estimation accuracy and reduce computation costs. Finally, the effectiveness of our proposed method is validated through numerical simulation tests using nonlinear Hammerstein models with Gaussian noise, reflecting complex stochastic industrial processes.

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Section: System Statementmentioning

confidence: 99%

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

Liu,

Zhang,

Zhou

et al. 2024

Mathematics

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“…Therefore, given the system output distribution (18) and the target distribution ( 19) and (20), following the general PFD scheme Equation ( 17), the optimal distribution of the tracking controller is given by the following theorem.…”

Section: Fpd Control Solution For the Weight Dynamic Systemmentioning

confidence: 99%

“…Theorem 1. Under the PDF (18) describing the dynamic weights of the system, the optimal controller distribution for minimising the performance index function ( 17) is given as follows:…”

Section: Fpd Control Solution For the Weight Dynamic Systemmentioning

confidence: 99%

“…In summary, based on the aforementioned problems, the challenges of stochastic systems include, but are not limited to the following: (1) most existing stochastic control algorithms are limited to the Gaussian assumption and have poor control performance once the systems contain non-Gaussianity or nonlinearity; (2) for the published control frameworks under the B-spline approximation model proposed by Wang [8], even though they have successfully lifted the Gaussian assumption of the traditional stochastic method, they have failed to involve the uncertainties and errors of the model parameters in a stochastic dynamical manner; (3) The majority of stochastic tracking problems consider static references other than the time-varying reference, which brings problems to practical applications. To address these issues, this paper proposes a novel B-spline model-based control framework using the fully probabilistic control design (FPD) [17,18]. In this method, a linear B-spline model is applied to describe the distribution of the system output [11,16].…”

Section: Introductionmentioning

confidence: 99%

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Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method

Zhang

Zhou

2023

Entropy

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Output probability density function (PDF) tracking control of stochastic systems has always been a challenging problem in both theoretical development and engineering practice. Focused on this challenge, this work proposes a novel stochastic control framework so that the output PDF can track a given time-varying PDF. Firstly, the output PDF is characterised by the weight dynamics following the B-spline model approximation. As a result, the PDF tracking problem is transferred to a state tracking problem for weight dynamics. In addition, the model error of the weight dynamics is described by the multiplicative noises to more effectively establish its stochastic dynamics. Moreover, to better reflect the practical applications in the real world, the given tracking target is set to be time-varying rather than static. Thus, an extended fully probabilistic design (FPD) is developed based on the conventional FPD to handle multiplicative noises and to track the time-varying references in a superior way. Finally, the proposed control framework is verified by a numerical example, and a comparison simulation with the linear–quadratic regulator (LQR) method is also included to illustrate the superiority of our proposed framework.

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“…Following this framework, Randa Herzallah and Yuyang Zhou have published a series of contributions in recent years. In particular, the PDF tracking control has been investigated for stochastic systems with input delay in [3,4]. To extend this result, the PDF tracking has been achieved for stochastic systems with both input delay and state delay in [5].…”

Section: Full Probability Design Using Kullback-leibler (Kl) Divergencementioning

confidence: 99%

Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

Zhang

Zhou

2022

IJNDI

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Survey/review study Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications Qichun Zhang 1, and Yuyang Zhou 2,* 1 Department of Computer Science, University of Bradford, Bradford BD7 1DP, United Kingdom 2 School of Computing, Engineering and the Built Environment, Edinburgh Napier University, Edinburgh EH10 5DT, United Kingdom * Correspondence: y.zhou@napier.ac.uk Received: 24 October 2022 Accepted: 18 November 2022 Published: 22 December 2022 Abstract: Non-Gaussian randomness widely exists in complex dynamical systems, in which the traditional mean-variance index cannot fully reflect the systematic characteristics. To improve the performance of control design subjected to non-Gaussian noises, stochastic distribution control (SDC) theory was proposed in the 1990s, where the output probability density function (PDF) has been investigated as an additional system variable. Following this framework, SDC has been extended to other research subjects in control systems such as filter design, fault diagnosis, and so on. It shows that SDC supplies an important solution to enhance the accuracy of system design, which is further beneficial to almost all the topics subject to non-Gaussian randomness. Meanwhile, the theoretical results of the SDC have been applied to several practical industrial applications. As data science raises based on the development of industrial artificial intelligence, SDC has been further developed recently focusing on data-driven design and multi-agent systems. To explore the new challenges with the evolution of SDC, e.g. unknown system models, unknown noise distributions, strong non-stationary transient dynamics, stability analysis and industrial applications, this survey summarises the most recent published results in the last 5 years of SDC work in terms of modelling, control, filtering, fault diagnosis, and industrial applications. Based on the technical analysis, potential future work is discussed in the end.

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A fully probabilistic control framework for stochastic systems with input and state delay

Cited by 5 publications

References 37 publications

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

Tracking Control for Output Probability Density Function of Stochastic Systems Using FPD Method

Recent Advances in Non-Gaussian Stochastic Systems Control Theory and Its Applications

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