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State estimation for distributed-parameter system

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PROGRESS IN NATURAL SCIENCE 1996年第1期6卷 115-119页

作者： Huo, WJ Yuan, WK

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State estimation for distributed-parameter system——Invariant embedding

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Progress in Natural Science:Materials International 1996年第1期 117-121页

作者：霍文军袁渭康 China East China University of Science and Technology Shanghai 200237 Unilab Research Center of Chemical Reaction Engineering

State estimation of distributed-parameter system is a prerequisite of optimal control for systems of this kind. In chemical industry, a number of reactors belong to distributed-parameter system, among which the fixed-bed reactor is a typical one. Nevertheless, only very much limited state variable measurements are allowed in industrial practice. In addition, time delay of the determination is commonly inevitable. The goal of state estimation for a dynamic system is focused on a quick and accurate approach to the

关键词： state estimation invariant embedding distributed parameter system fixed-bed reactor.

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Variable　Structure　Control　of　distributed　parameter　systems　and　Application　to　the　system　of　Heat　Process

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systems Science and systems Engineering 1994年第3期4卷 257-262页

作者： ZHAO Wenrong Department of Mathematics,Ningxia Education College,Yinchuan,750002 HOU Xuezhang Department of Mathematics,Northeast Normal University,Changchun,130024

The variable structure control problems of distributed parameter system are in vestrigated in this *** the conditions more general than in[1],[2],the equivalent, control theorem is ***,as an application to system of heat process,we give some conditons for sliding model such that the solution of system of heat process is exonentially stable unde the variable structure control.

关键词： distributed parameter system sliding mode variable structure control heat process

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ON THE DESIGN OF CONTROLLER FOR distributed parameter-systemS OF PARABOLIC TYPE - APPLICATION TO A ONE-DIMENSIONAL HEAT-CONDUCTION system

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KAGAKU KOGAKU RONBUNSHU 1987年第2期13卷 145-151页

作者： MATSUMOTO, S YOSHIDA, M Dept. of Chem. Eng. Tohoku Univ. Sendai 980 Japan

A simple procedure for the design of a controller for diffusion processes is presented, based on the decoupled state space model reduced by the finite Fourier transform technique. A Kalman filter is used to estimate the state variables to be provided for state feedback. A control system involving state estimation is implemented to control axial temperature distributions in an experimental heat conduction process. It is demonstrated that the state estimator produces a good estimate, even with very few sensors, and therefore control performance is satisfactory. © 1987, The Society of Chemical Engineers, Japan. All rights reserved.

关键词： distributed parameter system Eigenfunction Heat Conduction Kalman Filter Process Control State Estimation

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JOURNAL OF DIFFERENTIAL EQUATIONS 2025年 432卷

作者： Wang, Xiaoying Li, Yong Ji, Shuguan Jilin Univ Sch Math Changchun 130012 Peoples R China Northeast Normal Univ Ctr Math & Interdisciplinary Sci Changchun 130024 Peoples R China Northeast Normal Univ Sch Math & Stat Changchun 130024 Peoples R China

The relationship between two distributed parameter systems can be linked by a homeomorphic mapping, and the core is to study the minimizer of the functional to measure the degree of their similarity. We prove the existence and the necessary conditions (a maximum principle) for the minimizer. The similarity degree between two distributed parameter systems is thus defined by the functional, which extends the conjugacy in dynamical systems. As applications, we consider parabolic systems that satisfy different similarities. We prove a Hartman-Grobman theorem for general parabolic systems. We also demonstrate asymptotic similarity for the general quasilinear parabolic systems, indicating the Clausius statement of the second law of thermodynamics. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Similarity Conjugacy distributed parameter system Maximum principle Parabolic system

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Spatial graphic relation-based spatiotemporal fuzzy model for large-region distributed parameter systems and its application in lithium-ion batteries

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ENERGY 2025年 324卷

作者： Xu, Bowen Yang, Weiqi Lu, Xinjiang Bai, Yunxu Natl Univ Def Technol Hyperson Technol Lab Changsha Peoples R China Cent South Univ Coll Mech & Elect Engn State Key Lab Precis Mfg Extreme Serv Performance Changsha Peoples R China Univ South China Sch Elect Engn Hengyang Peoples R China

Many thermal processes, described by distributed parameter systems (DPSs), work in a large-scale operation region. In each region, it has special nonlinear dynamics due to specific relative position with heat sources. Achieving a global dynamic model of this kind of processes is extremely difficult due to different local dynamic features. Here, a spatial graphic relation-based spatiotemporal fuzzy modeling method is proposed to reconstruct the model of the large-region DPSs. First, a spectral clustering strategy is developed for region division, where the large-scale spatiotemporal region is divided into several local regions. For each local region, the spatial basis functions (SBFs) are extracted to represent the energy exchange on space. To reflect the global spatial feature, an incremental fuzzy fusion approach is designed and integrates these SBFs to form a global spatial function. Then, the temporal dynamics is obtained by projecting the spatiotemporal data on this global spatial function and characterized by a fuzzy model. Integrating the global spatial function and temporal model, the spatiotemporal model is constructed for the process with large-scale operation region. Using theoretical analysis and experiment, modeling ability of the proposed model is demonstrated effectively.

关键词： distributed parameter system Spectral clustering Fuzzy model Thermal processes Lithium-ion battery

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Online Three-Dimensional Fuzzy Multi-Output Support Vector Regression Learning Modeling for Complex distributed parameter systems

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APPLIED SCIENCES-BASEL 2025年第5期15卷 2750-2750页

作者： Zhou, Gang Zhang, Xianxia Yuan, Hanyu Wang, Bing Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200444 Peoples R China Jiangsu Co Ltd China Mobile Grp Nanjing 223800 Peoples R China

Complex distributed parameter systems (DPSs) are prevalent in numerous industrial processes. However, the nonlinear spatiotemporal dynamics inherent in DPS present significant challenges for accurate modeling. In this paper, an innovative online three-dimensional (3D) fuzzy multi-output support vector regression learning method is proposed for DPS modeling. The proposed method employs spatial fuzzy basis functions from the 3D fuzzy model as kernel functions, enabling direct construction of a comprehensive fuzzy rule base. parameters C and epsilon in the 3D fuzzy model adaptively adjust according to data sequence variations, effectively responding to system dynamics. Furthermore, a stochastic gradient descent algorithm has been implemented for real-time updating of learning parameters and bias terms. The proposed method was validated through two typical DPS and an actual rotary hearth furnace industrial system. The experimental results show the effectiveness of the proposed modeling method.

关键词： distributed parameter system fuzzy model support vector regression online model stochastic gradient descent

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Adaptive Learning Control for DPS With Continually Emerging Operational Conditions

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 3671-3684页

作者： Zhang, Yunfeng Yang, Chunhua Huang, Keke Wu, Dehao Gui, Gui Gui, Weihua Cent South Univ Sch Automat Changsha 410083 Peoples R China

During the operation of a distributed parameter system (DPS), its working conditions typically undergo dynamic changes. Although online learning methods can enable models to adapt to new working conditions to some extent, they often confront the "catastrophic forgetting" problem, where the updated model forgets historical working conditions. On the other hand, only a few new samples can be collected during online operation, and the sparse samples make it difficult to establish accurate models for new working conditions. Therefore, achieving precise control under full working conditions remains a challenging problem. To address these challenges, this paper proposes an adaptive predictive control method based on continuous learning that achieves stable control under full working conditions by continuously identifying working conditions and triggering adaptive model updates in real time. Specifically, a spatial-temporal feature-based working condition identification method is first proposed to identify changes in working conditions automatically. Then, to address the challenge of limited data for model updating, a parameter transfer method is proposed. Simultaneously, to ensure that the updated model retains the ability to characterize historical working conditions, an Elastic Weight Consolidation (EWC) constraint is incorporated into the loss function, thus overcoming the catastrophic forgetting problem, and ensuring the updated model can represent both the historical and new working conditions. Finally, by incorporating this condition identification mechanism and adaptive predictive model into the model predictive control framework, continuous precise control of DPS can be achieved. To demonstrate the superiority of the proposed method, extensive experiments are designed. Experimental results show that the proposed method can accurately identify new working conditions and learn new condition models with only a few online samples while overcoming model mismatch of his

关键词： Employee welfare Data models Adaptation models Predictive models Mathematical models Control systems Learning systems distributed parameter system model predictive control spatial-temporal characteristics continual learning model updating

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Sampled-data control of an unstable cascaded heat-heat system with different reaction coefficients

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AUTOMATICA 2025年 171卷

作者： Tang, Jia-Qi Wang, Jun-Min Kang, Wen Beijing Inst Technol Sch Math & Stat MIIT Key Lab Math Theory & Computat Informat Secur Beijing 100081 Peoples R China

The present paper is devoted to sampled-data control design of a PDE-PDE cascade system. These PDEs are governed by heat equations with different reaction coefficients. In order to stabilize the cascaded heat-heat system, we start with the design of continuous-time feedback control law. Then sampled-data control is further proposed for practical reasons. Sufficient conditions are derived for guaranteeing the exponential stability and well-posedness of the corresponding closed-loop system via Lyapunov method and modal decomposition method. Numerical examples illustrate the efficiency of the proposed method. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Cascaded heat-heat system distributed parameter system Modal decomposition approach Exponential stability Sampled-data control

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Adaptive Fault Tolerant Consensus Tracking Control for Flexible Manipulators MASs With Input Quantization and Time-Varying Delay

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第6期55卷 2597-2607页

作者： Zhao, Wei Li, Xing Liu, Yu Li, Zhijun South China Univ Technol Sch Automat Sci & Engn Guangzhou 510640 Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind SAPI Shenyang 110819 Peoples R China Dongguan Univ Technol Sch Elect Engn & Intelligentizat Dongguan 523808 Peoples R China Tongji Univ Sch Mech Engn Shanghai 200092 Peoples R China Shanghai Key Lab Wearable Robot & Human Machine In Shanghai 201804 Peoples R China

This article mainly investigates the problem of vibration suppression and angle cooperative tracking control of a multiple flexible manipulators described by partial differential equations (PDEs) with input quantization, actuator failures, and unmodeled system dynamics. An intermediate control law is designed, and a smooth function with a positive integrable time-varying function is introduced. Besides, a new smooth function is constructed in the control law to handle the influence of quantization and actuator faults. Under the designed controller, the angles of all flexible manipulators can reach consensus through mutual communication, and the elastic deformation of each flexible manipulator can also be suppressed. Furthermore, the asymptotic stability of a closed-loop system is realized based on the Lyapunov function. Finally, numerical simulation validates the effectiveness of the method.

关键词： Quantization (signal) Vibrations Fault tolerant systems Fault tolerance Adaptive systems Actuators Manipulator dynamics Fuzzy logic Consensus control Adaptive control Actuator faults consensus tracking control distributed parameter system input quantization vibration suppression

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