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Diophantine Equation and the Euclidean Algorithm: Methods and Philosophy of the Algebraic Approach to Linear Multivariable Control

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IEEE Control Systems 2025年第3期45卷 56-64页

作者： Vardulakis, Antonis I. G. Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang China

The story behind the Euclidean algorithm and its relationship to the solution of the Diophantine equation is examined in this article. The Euclidean algorithm appears in Proposition 2 in Book 7 of Euclid’s The Elements. This article explores the relationship between some of the concepts and procedures that appear in this Proposition and the ideas and mathematical tools used in linear multivariable control. In particular, its relationship to the solution of the so-called Diophantine equation for polynomial matrices and the problem of the existence and computation of stabilizing controllers for linear multivariable systems (LMSs) is revealed. The results and tools related to the algebraic structure of polynomial matrix models of LMSs that are useful for the numerical solution of the Diophantine equation for polynomial matrices are stated and demonstrated by a simple example. © 1991-2012 IEEE.

关键词： Polynomials

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Feedback Optimization of Nonlinear Strict-Feedback Systems

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Journal of Systems Science & Complexity 2025年第2期38卷 717-738页

作者： LIU Tong LIU Tengfei JIANG Zhong-Ping Department of Electrical and Computer Engineering New York University State Key Laboratory of Synthetical Automation for Process Industries Northeastern University

Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system's real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method.

关键词： Feedback optimization internal model output regulation small-gain theorem

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Intelligent recognition of steel plate surface defect based on deep convolutional GAN

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Neural Computing and Applications 2025年第14期37卷 8331-8345页

作者： Jiang, Benyi Zhou, Ping Sun, Xiaoyang Chai, Tianyou State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 Thailand

The production of hot rolled strip steel plates is affected by various uncertainties, resulting in numerous defects on the steel plate surface, such as scratches, cracks, and inclusions, which significantly impact the surface quality and performance of the steel plates. Considering the high rates of missed and false detections by traditional manual visual inspections, along with the limited accuracy of existing defect recognition algorithms due to insufficient defect sample data, a novel intelligent identification method is proposed for the recognition of steel plate surface defects based on deep convolutional generative adversarial network (DCGAN). Aiming at the problem of insufficient samples of actual industrial surface defect images, the proposed method generates steel plate surface image data with a similar distribution to real data based on DCGAN, which will expand the original sample data. Moreover, batch normalization is used to process the data, and an appropriate activation function is selected to better combine the original GAN and the deep convolutional neural network (DCNN) model in structure, thereby effectively improving the quality of the generated image data. Finally, the extended dataset is used to train the DCNN, and the recognition accuracy of the trained model on the test set is 96.16%. To the high error rate of manual inspection and the difficulty of creating and labeling datasets, the experimental results on actual industrial data demonstrate that the proposed method has good engineering application for the recognition of steel plate surface defects. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： Hot rolling

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Stacked semi-supervised autoencoder-regularized RVFLNs for reliable prediction of molten iron quality in blast furnace

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Neural Computing and Applications 2025年第17期37卷 10425-10438页

作者： Zhou, Ping Zhao, Peng Ou, Zihui Chai, Tianyou State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China

This paper proposes a novel stacked semi-supervised autoencoder-regularized random vector functional-link networks (RVFLNs) for reliable prediction of molten iron quality (MIQ) in blast furnace (BF) ironmaking. First, in order to accurately describe the importance of different process variables on the multivariate MIQ indices, an attention mechanism based on feedforward compensation is introduced. The mechanism is embedded at the front end of the stacked semi-supervised autoencoder deep network. Secondly, to extract the deep feature information which is closely related to the prediction target from the process data, a deep network structure composed of multiple semi-supervised autoencoder models is introduced. The output of the last hidden layer is then used as the input of the subsequent prediction model. At the same time, two regularization terms L1 and L2 are incorporated into RVFLNs to sparse network output weights and improve the robustness of modeling, aiming to solve the multicollinearity and overfitting problems of the basic RVFLNs. Experiments using the standard dataset and actual industrial data of BF demonstrate that the proposed method has good performance. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.

关键词： Blast furnaces

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Singularity-Free Low-Complexity Fault-Tolerant Prescribed Performance Control for Spacecraft Attitude Stabilization

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IEEE Transactions on automation Science and Engineering 2025年 22卷 15408-15419页

作者： Zhang, Jin-Xi Liu, Yun-Qi Chai, Tianyou Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110819 China

This paper is concerned with the problem of fault-tolerant prescribed performance attitude stabilization for spacecraft under model uncertainties and actuator failures. In most of the existing control designs for spacecraft described by the unit quaternion, the possible singularity issue of the virtual control coefficient matrix is neglected such that the controllability of the attitude subsystem cannot be warranted throughout. On the other hand, the related works depend on complex algorithms of approximation, estimation or diagnosis to deal with unknown system dynamics. In this paper, a singularity-free low-complexity fault-tolerant prescribed performance control (PPC) strategy is put forward. To exclude the singularity issue, an initialization principle of the performance envelope is devised. On this basis, a static PPC law is developed, without parameter identification, function approximation, disturbance estimation, failure detection, failure isolation, failure estimation. In place of the classical Lyapunov stability theory, a unified performance analysis framework based on proof by contradiction and the barrier Lyapunov function is constructed. It not only turns out attitude stabilization with the preassigned settling time and accuracy whenever the actuator failures happen, but also discloses the intrinsic robustness of the control system versus actuator failures and model uncertainties. A comparative study on a rigid spacecraft is performed to demonstrate the validity and advantage of our approach. © 2004-2012 IEEE.

关键词： Controllability

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Optical fiber sensors for heavy metal ion sensing

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Journal of Materials Science & Technology 2024年第22期189卷 110-131页

作者： Rao Fu Xiaobing Chen Xin Yan Haihui Li Taotao Hu Luo Wei Yuhan Qu Tonglei Cheng College of Information Science and Engineering State Key Laboratory of Synthetical Automation for Process IndustriesNortheastern UniversityShenyang 110819China

The ecological environment suffers from multiple pollution from many aspects,and the heavy metal ions(HMI)pose a significant threat to human *** these ions is challenging due to their trace amounts and diverse *** fiber sensors offer numerous advantages over conventional techniques in HMI sensing,including small size,quick response,resistance to electromagnetic interference,and long-range monitoring *** this paper,several optical methods for HMI detection have been described,namely fluorescence,fiber grating,fiber modal interference,surface plasmon resonance,and optical *** principles,structures,and sensitive materials of these methods are discussed in *** advantages and disadvantages of each approach are illustrated to facilitate a better ***,the current status and future directions for the development of HMI optical fiber sensors are also discussed,which could enlighten the future HMI sensor design.

关键词： Heavy metal ion Optical fiber Trace amount detection Fiber sensor

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Cascaded four-wave mixing all-optical wavelength converter based on highly nonlinear fiber deposited graphene oxide

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Journal of Materials Science & Technology 2024年第4期171卷 10-15页

作者： Yuanhongliu Gao Xiaoyu Chen Tonglei Cheng Fang Wang Xin Yan College of Information Science and Engineering State Key Laboratory of Synthetical Automation for Process IndustriesNortheastern UniversityShenyang 110819China

The all-optical wavelength conversion using cascaded four-wave mixing(FWM)phenomena with graphene oxide(GO)and a highly nonlinear fiber(HNLF)device is demonstrated *** has a strong third-order nonlinear effect and is an excellent nonlinear optical material for nonlinear optical wavelength *** group velocity matching of pump and signal,HNLF,and GO amplification promote the cascaded nonlinear frequency mixing *** the experimental and analytical results,the maximum spacing between signal and pump is 21 nm,and specifically,the order of cascaded FWM light increases from order 1 to order 2 with increasing GO,and the first-order FWM conversion effi-ciency increases to a maximum of−14.5 *** the best of our knowledge,this is the first time that cascaded FWM-based all-optical wavelength conversion in HNLF-GO with wide wavelength selectivity is investigated with combined pump and signal *** findings not only provide an effective method for achieving all-optical wavelength conversion in cascaded FWM but also offer the possibility of fabricating high-performance nonlinear optical devices.

关键词： Four-wave mixing Graphene oxide Highly nonlinear fiber Optical wavelength conversion

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Hybrid Intelligent Optimization of Nonlinear Switched Systems With Guaranteed Feasibility

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2024年第10期5卷 5244-5257页

作者： Li, Huan Fu, Jun Chai, Tianyou Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang100819 China

To address the challenge of globally optimal control of path-constrained switched systems, a hybrid intelligent dynamic optimization method is proposed by combining the biobjective particle swarm optimization (PSO) method and a gradient descent method, which simultaneously obtains globally optimal switching instants and input and guarantees rigorous satisfaction of the path constraints over the continuous time horizon. First, the path constraint of switched systems is discretized into multiple point constraints, and then the right-hand side of the path constraint (≤ 0) is substituted with a negative value (≤-ϵ). Second, the single-objective constrained dynamic program of switched systems is transformed into a biobjective unconstrained dynamic program where each particle intelligently adjusts its objectives to detect the global optimum area satisfying the constraints, depending on its current position in the search space by the search mechanism of PSO. Third, the deterministic optimization method is deployed in the detected global optimum area to locate a feasible solution satisfying the Karush-Kuhn- Tucker (KKT) conditions to a specified tolerance of dynamic optimization of switched systems. Moreover, it is proved that the hybrid intelligent dynamic optimization method can obtain the optimal solution satisfying the first-order approximation KKT conditions within a finite number of iterations. Finally, the results of numerical simulations show the effectiveness of the presented method in terms of improving the solution accuracy and guaranteeing rigorous satisfaction of the path constraint. Impact statement-The optimization methods of pathconstrained switched systems can be broadly categorized into two groups: deterministic optimization and heuristic optimization methods. Deterministic optimization methods can guarantee that the path constraint is feasible within a finite number of iterations, but the obtained solution can easily fall into a local optimum. On the cont

关键词： Heuristic algorithms

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Prefetching-based Multiproposal Markov Chain Monte Carlo Algorithm

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2024年第9期5卷 4493-4505页

作者： Ye, Guifeng Lu, Shaowen Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang110819 China

Our proposed algorithm is a prefetching-based multiproposal Markov Chain Monte Carlo (PMP-MCMC) method that efficiently explores the target distribution by combining multiple proposals with the concept of prefetching. In our method, not all proposals are directly derived from the current state;some are derived from future states. This approach breaks through the inherent sequential characteristics of traditional MCMC algorithms. Compared with single-proposal and multiproposal methods, our approach speeds up by K times and the burn-in period is reduced by a factor of 1/log2K maximally, where K is the number of parallel computational units or processing cores. Compared with prefetching method, our method has increased the number of samples per iteration by a factor of K/log2K. Furthermore, the proposed method is general and can be integrated into MCMC variants such as Hamiltonian Monte Carlo (HMC). We have also applied this method to optimize the model parameters of neural networks and Bayesian inference and observed significant improvements in optimization performance. © 2020 IEEE.

关键词： Monte Carlo methods

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An Improved Continuous-Encoding-Based Multiobjective Evolutionary Algorithm for Community Detection in Complex Networks

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2024年第11期5卷 5815-5827页

作者： Fu, Jun Wang, Yan Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Shenyang100819 China

Community detection is a fundamental and widely studied field in network science. To perform community detection, various competitive multiobjective evolutionary algorithms (MOEAs) have been proposed. It is worth noting that the latest continuous encoding (CE) method transforms the original discrete problem into a continuous one, which can achieve better community partitioning. However, the original CE ignored important structural features of nodes, such as the clustering coefficient (CC), resulting in poor initial solutions and reduced the performance of community detection. Therefore, we propose a simple scheme to effectively utilize node structure feature vectors to enhance community detection. Specifically, a CE and CC-based (CE-CC) MOEA called CECC-Net is proposed. In CECC-Net, the CC vector performs the Hadamard product with a continuous vector (i.e., a concatenation of the continuous variables x associated with the edges), resulting in an improved initial individual. Then, applying the nonlinear transformation to the continuous-valued individual yields a discrete-valued community grouping solution. Furthermore, a corresponding adaptive operator is designed as an essential part of this scheme to mitigate the negative effects of feature vectors on population diversity. The effectiveness of the proposed scheme was validated through ablation and comparative experiments. Experimental results on synthetic and real-world networks demonstrate that the proposed algorithm has competitive performance in comparison with several state-of-the-art EA-based community detection algorithms. © 2024 IEEE.

关键词： Vectors

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