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Quasi-bipartite synchronisation of multiple inertial signed delayed neural networks under distributed event-triggered impulsive control strategy

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IET CONTROL theory AND applications 2021年第12期15卷 1615-1627页

作者： Udhayakumar, K. Rihan, Fathalla A. Li, Xiaodi Rakkiyappan, R. Bharathiar Univ Dept Math Coimbatore Tamil Nadu India UAE Univ Coll Sci Dept Math Sci Al Ain 15551 U Arab Emirates Shandong Normal Univ Sch Math & Stat Jinan Peoples R China

The central concern of this paper is to study leader-following quasi-bipartite synchronisation of a multiple inertial signed neural networks with varying time-delay by utilising distributed event-triggered impulsive control scheme, where connections between adjacent nodes of the neural networks either positive or negative. The second-order neural networks, called inertial neural networks, can be transformed into differential equations of first-order by implementing suitable variable substitution. Under certain hypothesis about the node dynamics, signed graph theory and balanced topology of networks, some conditions are derived in terms of lower-dimensional linear matrix inequalities (LMIs) to achieve leader-following quasi-bipartite synchronisation. In addition, a basic algebraic condition is derived to estimate the theoretical upper bound for the error node. Finally, some numerical simulations are provided to illustrate the correctness of the theoretical results.

关键词： differential equations algebra multiple inertial signed neural networks perturbation techniques signed graph theory leader-following neural nets quasibipartite synchronisation time-varying systems Combinatorial mathematics second-order neural networks Stability in control theory control system synthesis synchronisation distributed event-triggered impulsive control scheme Control system analysis and synthesis methods called inertial neural networks graph theory algebra delays Lyapunov methods linear matrix inequalities nonlinear dynamical systems time-delay distributed event-triggered impulsive control strategy asymptotic stability periodic control

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Largest Angle Path Distance for Multi-Manifold Clustering

Largest Angle Path Distance for Multi-Manifold Clustering

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2023 International conference on Sampling theory and applications, SampTA 2023

作者： Chen, Haoyu Little, Anna Narayan, Akil University of Utah Department of Mathematics Salt Lake CityUT84112 United States University of Utah Utah Center for Data Science Department of Mathematics Salt Lake CityUT84112 United States University of Utah Scientific Computing & Imaging Inst. Department of Mathematics Salt Lake CityUT84112 United States

ISBN: (纸本)9798350328851

We propose a novel, angle-based path metric for the multi-manifold clustering problem. This metric, which we call the largest-angle path distance (LAPD), is computed as a bottleneck path distance in a graph constructed on d-simplices of data points. When data is sampled from a collection of d-dimensional manifolds which may intersect, the method can cluster the manifolds with high accuracy and automatically detect how many manifolds are present. By leveraging fast approximation schemes for bottleneck distance, this method exhibits quasi-linear computational complexity in the number of data points. In addition to being highly scalable, the method outperforms existing algorithms in numerous numerical experiments on intersecting manifolds, and exhibits robustness with respect to noise and curvature in the data. © 2023 IEEE.

关键词： numerical methods

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A new nonstationary preconditioned iterative method for linear discrete ill-posed problems with application to image deblurring

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numerical linear algebra WITH applications 2021年第2期28卷

作者： Buccini, Alessandro Donatelli, Marco Reichel, Lothar Zhang, Wei-Hong Univ Cagliari Dept Math & Comp Sci Cagliari Italy Univ Insubria Dept Sci & High Technol Como Italy Kent State Univ Dept Math Sci Kent OH 44242 USA Lanzhou Univ Sch Math & Stat Lanzhou Peoples R China

Discrete ill-posed inverse problems arise in many areas of science and engineering. Their solutions are very sensitive to perturbations in the data. Regularization methods aim at reducing this sensitivity. This article considers an iterative regularization method, based on iterated Tikhonov regularization, that was proposed in M. Donatelli and M. Hanke, Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring, Inverse Problems, 29 (2013), Art. 095008, 16 pages. In this method, the exact operator is approximated by an operator that is easier to work with. However, the convergence theory requires the approximating operator to be spectrally equivalent to the original operator. This condition is rarely satisfied in practice. Nevertheless, this iterative method determines accurate image restorations in many situations. We propose a modification of the iterative method, that relaxes the demand of spectral equivalence to a requirement that is easier to satisfy. We show that, although the modified method is not an iterative regularization method, it maintains one of the most important theoretical properties for this kind of methods, namely monotonic decrease of the reconstruction error. Several computed experiments show the good performances of the proposed method.

关键词： discrete ill‐ posed inverse problems iterated Tikhonov method spectral equivalence

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Elastic Stabilization Control for Polynomial Parameter-varying Systems with applications to a Turbofan Engine

Elastic Stabilization Control for Polynomial Parameter-varyi...

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Control theory and applications (ICoCTA), International conference on

作者： Chuzheng Su Jialin Chen Shenghua Wu Jianping Zeng School of Aerospace Engineering Xiamen University Xiamen China

ISBN: (数字)9798331506155

ISBN: (纸本)9798331506162

Aiming at the problem of the controller parameter perturbation and exponential stabilization of controlled plants in complex working environments, an elastic stabilization control method, which is based on polynomial parameter-varying (PPV) model is proposed. To address the parameter perturbation problem of controller in the controlled plants, the conditions for the existence of the elastic controller that ensures the exponential stability of the PPV systems are derived using Lyapunov stability theory and state-and-parameter-dependent (SPD) linear matrix inequalities. The controller is solved by using the sum of squares (SOS) convex optimization technique. Finally, the proposed method is applied to the control problem of PPV model of turbofan engine. The numerical simulation results show that the designed controller has good control performance, and is robust in the large envelope range of the engine.

关键词： Stability Perturbation methods Process control Polynomials Convex functions Control theory linear matrix inequalities Closed loop systems Engines Lyapunov methods

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Distributed event-triggered output feedback H∞ control for multi-agent systems with transmission delays

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IET CONTROL theory AND applications 2021年第12期15卷 1646-1660页

作者： Li, Yanjin Yu, Hui Xia, Xiaohua China Three Gorges Univ Coll Sci Yichang Peoples R China Univ Pretoria Dept Elect Elect & Comp Engn Ctr New Energy Syst Pretoria South Africa

The output feedback H infinity consensus control problem of multi-agent systems is studied using an event-triggered control strategy. Two types of transmission delays, one from the system output to the output feedback controller (OFC) and the other from the OFC to the zero-order holder, are considered. This causes the OFC and the system not to be updated in the same time intervals. An interval dividing approach is applied to such that the whole system can be updated in the same time intervals. An event-triggered OFC with H infinity performance is proposed for multi-agent systems to achieve consensus. By constructing an appropriate Lyapunov-Krasovskii functional, sufficient conditions based on linear matrix inequality are derived to guarantee the consensus achievement. Finally, the theoretical results are validated using computer simulation.

关键词： multiagent systems event-triggered control strategy output feedback H∞ consensus control problem multi-agent systems Multivariable control systems time-varying systems Time-varying control systems system output control system synthesis Stability in control theory Control system analysis and synthesis methods distributed event-triggered output feedback H output feedback controller time intervals distributed control feedback linear algebra (numerical analysis) Lyapunov methods delays linear matrix inequalities transmission delays event-triggered OFC Distributed parameter control systems asymptotic stability

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A New Augmented Observable Canonical Form and Its applications 35

A New Augmented Observable Canonical Form and Its Applicatio...

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35th Chinese Control and Decision conference (CCDC)

作者： Zhou, Fan Shen, Yanjun Tan, Chao China Three Gorges Univ Coll Elect Engn & New Energy State Grid Hubei Direct Current Operat Res Inst Yichang Peoples R China China Three Gorges Univ Coll Elect Engn & New Energy Yichang Peoples R China

ISBN: (纸本)9798350334722

In this paper, a new augmented observable canonical form is presented and applied to observer design for both linear and nonlinear systems with uncertain measurement disturbance. In order to analyse the effect of the disturbance to the estimation errors, we propose a novel analytical method with some tunable parameters. For any kinds of measurement disturbance, by tuning these parameters, it is shown that some estimation errors can converge to an arbitrarily small neighborhood of the origin. It is also shown that the augmented high-gain observer has low sensitivity to measurement noise, especially for high dimension nonlinear systems. Finally, a numerical simulation is offered to confirm the validity of the proposed methods.

关键词： measurement noises augmented observable canonical form augmented observer high-gain filter sensitivity

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Event-triggered Bounded Synchronization Control for Heterogeneous Complex Networks

Event-triggered Bounded Synchronization Control for Heteroge...

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Fully Actuated System theory and applications (CFASTA), conference on

作者： Zhentao Wang Ling Huang Yunfei Wang Bing Li School of Automation Harbin University of Science and Technology Harbin China

ISBN: (数字)9798350373691

ISBN: (纸本)9798350373707

An event-triggered bounded synchronization of heterogeneous complex networks is studied. Firstly, a distributed full-dimensional state observer is designed for each node in the heterogeneous complex network to reconstruct the system state. The joint error system of observation and synchronization errors is obtained, and an event-triggered controller based on the observer state is designed. Then, by using the Lyapunov stability theory, a sufficient condition is derived to ensure the bounded stabilization of the joint error system. After that, the observer gain, controller gain, and event-triggered parameters are jointly solved using linear Matrix Inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed synchronization theory.

关键词： Sufficient conditions Uncertainty Complex networks Observers linear matrix inequalities Synchronization Lyapunov methods

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linear convergence of a proximal alternating minimization method with extrapolation for 1-Norm principal component analysis

Linear convergence of a proximal alternating minimization me...

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作者： Wang, Peng Liu, Huikang So, Anthony Man-Cho Department of Electrical Engineering and Computer Science University of Michigan Ann ArborMI48109 United States School of Information Management and Engineering Shanghai University of Finance and Economics Shanghai China Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Shatin NT Hong Kong Hong Kong

A popular robust alternative of the classic principal component analysis (PCA) is the \ell 1-norm PCA (L1-PCA), which aims to find a subspace that captures the most variation in a dataset as measured by the \ell 1-norm. L1-PCA has shown great promise in alleviating the effect of outliers in data analytic applications. However, it gives rise to a challenging nonsmooth, nonconvex optimization problem, for which existing algorithms are either not scalable or lack strong theoretical guarantees on their convergence behavior. In this paper, we propose a proximal alternating minimization method with extrapolation (PAMe) for solving a two-block reformulation of the L1-PCA problem. We then show that for both the L1-PCA problem and its two-block reformulation, the Kurdyka-\Lojasiewicz exponent at any of the limiting critical points is 1/2. This allows us to establish the linear convergence of the sequence of iterates generated by PAMe and to determine the criticality of the limit of the sequence with respect to both the L1-PCA problem and its two-block reformulation. To complement our theoretical development, we show via numerical experiments on both synthetic and real-world datasets that PAMe is competitive with a host of existing methods. Our results not only significantly advance the convergence theory of iterative methods for L1-PCA but also demonstrate the potential of our proposed method in applications. © 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.

关键词： Principal component analysis

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A Survey on Time Series Data Classification: Blockchain Technologies and Security Concerns 28th

A Survey on Time Series Data Classification: Blockchain Tech...

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28th International conference on Knowledge Based and Intelligent information and Engineering Systems, KES 2024

作者： Alsayyad, Ahmed Faris Abid Ali, Alaa Abid Muslam Mabrouk, Mohamed Al-Shammari, Ahmed Zrigui, Mounir Research Laboratory in Algebra Numbers Theory and Intelligent Systems RLANTIS University of Monastir Monastir Tunisia Department of Computer Science College of Computer Science and Information Technology University of Al-Qadisiyah Al Diwaniyah58002 Iraq Al-Qadisiyah University Al-Qadisiyah Iraq Military Academy Fondok Jedid Tunisia

The difficulties about user security and privacy have appeared as significant concerns in recent years. The number of cyber-attacks grows at a concerning velocity, hence rendering internet users susceptible to malicious activities perpetrated by hackers. Data mining approaches are employed to extract accurate results from massive and complex databases. Furthermore, the utilization of Blockchain (BC) approaches is increasingly popular in current Internet of Things (IoT) applications as an opportunity to address issues related to privacy and security. Lots of studies have been performed on algorithms for data mining and techniques concerning blockchain. Time series data is a commonly used form of data. Time Series Classification (TSC) refers to the creation of predictive models that generate a target variable or label based on linear or sequential data inputs across a considerable duration. The possible results may be presented in either ordinal or numerical form. Even so, previous studies have shown major limitations when it comes to handling privacy and security issues that can't be applicable in dynamic instances, as well as the substantial computational cost necessary. Moreover, correctly determining the amount of sensitive parameters required to complete the classification process remains a challenge. We have put forth a comprehensive survey on the classification of blockchain data. In the first phase of our study, we conducted an analysis and categorization of both conventional data classification approaches and contemporary time series data classification techniques. We further discussed limitations and strengths of existing techniques. Finally, we highlight future research problems and directions. © 2024 The Authors.

关键词： Differential privacy

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Robust estimation of the number of coherent radar signal sources using deep learning

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IET RADAR SONAR AND NAVIGATION 2021年第5期15卷 431-440页

作者： Rogers, John Ball, John E. Gurbuz, Ali C. Mississippi State Univ Elect & Comp Engn Starkville MS USA

A deep-learning-based approach to estimating the number of coherent sources in radar is presented. A proper estimate of the number of sources in a signal enables improved angle-of-arrival (AoA) estimation common in applications such as radar, sonar, and communication systems. Many AoA estimators utilised in these areas require accurate estimates of the number of sources for enhanced performance. Herein, a robust method that performs well under the existence of coherent sources is developed. The proposed method is based on deep learning and it is shown to perform better than state-of-the-art versions of the Akaike Information Criteria (AIC), Minimum Description Length (MDL), and Exponentially Embedded Families (EEF) estimators, which employ spatial smoothing of the covariance matrix to handle coherent signals.

关键词： radar signal processing Radar theory Minimum Description Length spatial smoothing linear algebra (numerical analysis) Signal processing and detection communication systems deep learning (artificial intelligence) radar computing Exponentially Embedded Families estimators Radar equipment, systems and applications AoA estimators Akaike Information Criteria Electrical engineering computing covariance matrix covariance matrices coherent radar signal sources estimation theory angle-of-arrival estimation smoothing methods deep learning-based approach robust estimation direction-of-arrival estimation Other topics in statistics

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