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43rd Annual Conference of the IEEE-Industrial-Electronics-Society (IECON)

作者： Zhang, Yunong Guo, Jinjin Zhang, Deyang Qiu, Binbin Yang, Zhi Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China Minist Educ Key Lab Autonomous Syst & Networked Control Guangzhou 510640 Guangdong Peoples R China SYSU CMU Shunde Int Joint Res Inst Foshan 528300 Peoples R China Minist Educ Key Lab Machine Intelligence & Adv Comp Guangzhou 510006 Guangdong Peoples R China

ISBN: (纸本)9781538611272

In this paper, the output tracking of time-varying linear system is investigated with pseudo division-by-zero phenomenon illustrated. We only use Zhang dynamics (ZD) to design a ZD tracking controller, which is easier than using Zhang-gradient (ZG) method. The purpose of output tracking control for the considered time-varying linear system is to make the actual output track the desired output with absolute error within an acceptably tiny error range;namely, the absolute error is as small as possible or even exponentially convergent to zero. By conducting controller design with ZD method as well as computer simulations, we can verify the efficacy of the proposed ZD controller in performing the output tracking control with the pseudo division-by-zero phenomenon illustrated. Besides, for the sake of comparative analysis of simulation results, we set the design parameters with different specific values. Anyhow, the output tracking of time-varying linear system can finally be achieved through simulation examples.

关键词： Output tracking time-varying linear system Pseudo division-by-zero Zhang dynamics (ZD)

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Sigmoid Function Aided Zhang Dynamics Control for Output Tracking of time-varying linear system with Bounded Input 35

Sigmoid Function Aided Zhang Dynamics Control for Output Tra...

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第35届中国控制会议

作者： ZHANG Yunong ZHANG Deyang QIU Bibbin WANG Jinjin LI Jian School of Information Science and Technology Sun Yat-sen University (SYSU) SYSU-CMU Shunde International Joint Research Institute Key Laboratory of Autonomous Systems and Networked Control Ministry of Education

ISBN: (纸本)9781509009107

This paper investigates the output-tracking control of time-varying linear（TVL） *** that the input is always limited in a range due to actuator physical constraints or energy-saving *** combining the Zhang dynamics（ZD） and the sigmoid function,an effective controller,termed sigmoid function aided ZD（SFAZD） controller,is designed for tracking the TVL *** verifications substantiate that the proposed SFAZD controller can achieve accurate tracking results,and limit the input in the range during the tracking process.

关键词： Tracking Control time-varying linear system Zhang Dynamics Sigmoid Function Bounded Input

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Non-uniformly exponential stability for time-varying continuous-time linear system

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2024年第18期47卷 14251-14262页

作者： Hu, Xiulin Wang, Lei Tian, Youjia Hefei Univ Sch Artificial Intelligence & Big Data Hefei 230601 Anhui Peoples R China

Exponential stability analysis is one of the most important problems in the study of the asymptotic behavior of solutions of continuous-time linear systems. In comparison with the classical exponential stability, weaker criteria of (strongly) non-uniformly exponential stability for the time-varying linear systems are derived in this paper. By a nonsingular linear state transformation, a (strongly) non-uniformly exponentially stable system can be equivalent to a simple one with the coefficient matrix whose measure is bounded by negative constants.

关键词： matrix measure non-uniformly exponential stability time-varying linear system

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Neural networks for total least squares solution of the time-varying linear systems

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COMPUTATIONAL & APPLIED MATHEMATICS 2025年第1期44卷 1-22页

作者： Wang, Xuezhong Shan, Jiali Wei, Yimin Hexi Univ Sch Math Zhangye 734000 Peoples R China Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China Fudan Univ Sch Math Sci Key Lab Math Nonlinear Sci Shanghai 200433 Peoples R China

In this paper, we consider the total least squares solution of time-varying linear systems with time-varying right-hand side vectors. The neural network model termed as the neural network model for solving time-varying total least squares problems (NNTVTLS) and its discrete form of the neural network model for solving time-varying total least squares problems (DNNTVTLS) are provided to solve this problem. The analyses of convergence and robustness demonstrate that the proposed DNNTVTLS model exhibits global convergence and superior noise immunity. Numerical experiments further verify the superiority and effectiveness of the DNNTVTLS model in solving time-varying linear equations, taking into account the presence of noise.

关键词： time-varying matrix time-varying linear system Total least squares solution Neural network model Convergence Robustness

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Gradient descent-based parameter-free methods for solving coupled matrix equations and studying an application in dynamical systems

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APPLIED NUMERICAL MATHEMATICS 2025年 212卷 29-59页

作者： Shirilord, Akbar Dehghan, Mehdi Amirkabir Univ Technol Tehran Polytech Fac Math & Comp Sci Dept Appl Math 424 Hafez Ave Tehran 15914 Iran

This paper explores advanced gradient descent-based parameter-free methods for solving coupled matrix equations and examines their applications in dynamical systems. We focus on the coupled matrix equations { AX+YB=C, DX+YE=F, where A, D E OR"x", B, E E OR"x", C, F E OR" x" are given matrices, and X, Y E OR" x" are the unknown matrices to be determined. We propose a novel gradient descent-based approach with parameter-free, enhancing convergence through an accelerated technique related to momentum methods. A comprehensive analysis of the convergence and characteristics of these methods is provided. Our convergence analysis demonstrates that if the spectrum of a block matrix constructed from the matrices A, B, D, and E is confined within a horizontal ellipse in the complex plane, centered at (0,0) with a major axis length of 3 and a minor axis length of 1, then the accelerated momentum method will converge to the exact solution of the discussed model. The numerical results indicate that proposed methods significantly improve efficiency, showing faster convergence and reduced computational time compared to traditional approaches. Additionally, we apply these methods to linear dynamic systems, demonstrating their effectiveness in real-world scenarios.

关键词： Gradient descent method Dynamical systems Momentum technique Control theory Discrete-time antilinear systems time-varying linear system Coupled matrix equation Parameter-free method Iterative method Hierarchical identification principle

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Explicit linear Left-and-Right 5-Step Formulas With Zeroing Neural Network for time-varying Applications

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第2期53卷 1133-1143页

作者： Yang, Min Zhang, Yunong Tan, Ning Hu, Haifeng Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Peoples R China Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Guangdong Acad Sci Inst Intelligent Mfg Guangdong Key Lab Modern Control Technol Guangzhou 510070 Peoples R China

In this article, being different from conventional time-discretization (simply called discretization) formulas, explicit linear left-and-right 5-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S formula with four variable parameters is developed first, and constraints of these four parameters are displayed to guarantee the zero stability, consistence, and convergence of the formula. Then, by choosing specific parameter values within constraints, eight specific sixth-order ELLR5S formulas are developed. The general sixth-order ELLR5S formula is further utilized to generate discrete zeroing neural network (DZNN) models for solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are also utilized. Theoretical analyses are presented to show the performance of ELLR5S formulas and DZNN models. Furthermore, abundant experiments, including three practical applications, that is, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulas as well as the corresponding DZNN models.

关键词： time-varying systems Manipulators Computational modeling linear systems Location awareness Numerical models Nonlinear systems Angle-of-arrival (AoA) localization explicit linear left-and-right 5-step (ELLR5S) formula redundant manipulator control time-varying linear system time-varying nonlinear system zeroing neural network (ZNN)

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Decomposition of Fourth-Order linear time-varying systems into its Third- and First-Order Commutative Pairs

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CIRCUITS systemS AND SIGNAL PROCESSING 2023年第6期42卷 3320-3340页

作者： Ibrahim, Salisu Koksal, Mehmet Emir Ondokuz Mayis Univ Dept Math TR-55139 Atakum Samsun Turkiye

The necessary and sufficient conditions for decomposing a fourth-order (FO) linear time-variant system (LTVS) in the form of cascade connection of a first-order system and a third-order system that are commutative are expressed explicitly in this paper. Some additional conditions are also derived for a valid decomposition when the initial conditions are different from zero. Further, explicit formulas are derived for the determination of the decomposed subsystems. The paper also investigated the effects of changing the connection order on the sensitivity and disturbance properties. Theoretical results about the decomposition are supported and illustrated by considering various examples.

关键词： Analog control Robust control time-varying linear system Differential equation Physical systems

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On the simultaneous stabilization for a family of time-varying linear systems under the transmission condition

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ASIAN JOURNAL OF CONTROL 2020年第5期22卷 1995-2003页

作者： Liu, Liu Lu, Yufeng Dalian Univ Technol Sch Math Sci Dalian Peoples R China

This paper deals with the simultaneous stabilization problem for a family of discrete time-varying linear systems in the framework of nest algebra. Under the transmission condition, a necessary and sufficient condition for simultaneous "stabilizability" is established in terms of single strong representation for only one controller in the transmission condition, in which the resulting characterization involves no strong representation of the plants compared to previous work.

关键词： nest algebra simultaneous stabilization time-varying linear system transitivity

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Matrix Pontryagin principle approach to controllability metrics maximization under sparsity constraints☆

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AUTOMATICA 2024年 164卷

作者： Ikeda, Takuya Ohtsuka, Tomofumi Kashima, Kenji Univ Kitakyushu Fac Environm Engn Fukuoka Japan Kyoto Univ Grad Sch Informat Kyoto Japan

This study considers optimization problems for time-varying network topologies that maximize the controllability of linear network systems under sparsity constraints. The major theoretical differences from the existing findings on control node scheduling problems is that our method is based on the matrix-valued Pontryagin maximum principle applied to the controllability Lyapunov differential equation. This allows us to handle various controllability metrics that can only be approximated by existing methods. Finally, we perform a numerical evaluation of our proposed method and compare results with those of our previous approximation method. (c) 2024 Elsevier Ltd. All rights reserved.

关键词： Convex relaxation Networked systems Node selection problem Optimal control Sparse control Sparse optimization time-varying linear system

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Optimal time-varying topology for network systems 13

Optimal time-varying topology for network systems

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13th Asian Control Conference (ASCC)

作者： Ikeda, Takuya Kashima, Kenji Univ Kitakyushu Fac Environm Engn Fukuoka 8080135 Japan Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan

ISBN: (纸本)9788993215236

This paper treats an optimization problem of time-varying network topology for continuous-time linear network systems. Although the topology from controllers to nodes has been widely investigated in the literature, this paper alternatively focuses on the topology among nodes. For the cost function, we employ the trace of the controllability Gramian to reduce the required control energy. For the constraint, we introduce an upper bound of the L-0 norm of the data transmission among nodes to find an effective communication schedule. Since the formulated optimization problem is combinatorial, we introduce a convex relaxation for its computational tractability. After reformulating the problem into an optimal control problem where Pontryagin's maximum principle can be applied, we give a sufficient condition under which the relaxation problem gives a solution of the original problem. We finally provide a numerical algorithm based on a derived optimality condition and illustrate the proposed method with an example.

关键词： convex relaxation networked systems optimal control sparse optimization time-varying linear system

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