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Derivation of fixed-interval smoothing algorithm using covariance information in distributed parameter systems

APPLIED MATHEMATICS AND COMPUTATION 2006年第2期176卷 662-672页

作者： Nakamori, S. Garcia-Ligero, M. J. Hermoso-Carazo, A. Linares-Perez, J. Kagoshima Univ Fac Educ Dept Technol Kagoshima 8900065 Japan Univ Granada Dept Estadist & Invest Operat E-18071 Granada Spain

This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the algorithm only requires the second-order moments of the signal and the white noise perturbing its observations. Practical application of the proposed algorithm is illustrated with a restoration image problem. (c) 2005 Elsevier Inc. All rights reserved.

关键词： fixed-interval smoothing distributed parameter systems covariance information recursive estimation Wiener-Hopf equation

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Assessment of severity of nonlinearity for distributed parameter systems via nonlinearity measures

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JOURNAL OF PROCESS CONTROL 2017年 58卷 1-10页

作者： Wu, Jigang Jiang, Mian Li, Xuejun Feng, Heying Hunan Univ Sci & Technol Hunan Prov Key Lab Hlth Maintenance Mech Equipment Xiangtan 411201 Peoples R China

The performance of controlled distributed parameter systems (DPSs) not only depends on the controller, but also on the dynamic nature of the process itself. One of the primary factors affecting DPS control is process nonlinearity. In many situations, the extent and severity of nonlinearity is the crucial characteristic in deciding whether linear system analysis and controller synthesis methods are adequate. However, due to their spatio-temporal coupling, traditional nonlinearity measures cannot be directly applied to nonlinear DPSs. In this study, a nonlinearity measure method to quantify the severity of nonlinearity for a class of DPSs is proposed. First, time/space separation and model reduction are carried out using proper orthogonal decomposition (POD). Thus, an optimal linear time-invariant model with a low-order is obtained through the optimization of a spatio-temporal error while full state feedback is incorporated in order to stabilize the linear model. Finally, nonlinearity quantification for DPSs is calculated using the obtained stable linear time-invariant system. The complexity of the calculations for nonlinearity measures is greatly reduced after the model reduction using POD. This method easily estimates the extent to which the process behavior deviates from linearity, which aids in determining whether a linear system analysis and controller synthesis methods are adequate. The nonlinearity quantification indicates that DPSs with smaller values are better approximated by a linear model than DPSs with larger values in the target time/space domain. The effectiveness of the proposed method is illustrated using two numerical examples. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Nonlinearity measure Proper orthogonal decomposition Particle swarm optimization

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A Spatiotemporal Neural Network Modeling Method for Nonlinear distributed parameter systems

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2021年第3期17卷 1916-1926页

作者： Lu, XinJiang Cui, Xiangbo Cent South Univ Sch Mech & Elect Engn State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China

Neural network (NN) has been widely used in the field of modeling of lumped parameter systems. However, an NN approach cannot be used to model complex nonlinear distributed parameter systems (DPSs) because it does not account for this type of system's relationship with space. In this article, we propose a novel spatiotemporal NN (SNN) method to model nonlinear DPSs, which considers not only nonlinear dynamics regarding time, but also a nonlinear relationship with space. A temporal NN model was first constructed to represent the nonlinear temporal dynamics of each sensor's position. A spatial distribution function was then developed to represent the nonlinear relationship between spatial points. This strategy results in inherent consideration of any spatial dynamics. Finally, by integrating both the temporal NN model and the spatial distribution function, a novel SNN model was created to represent the spatiotemporal dynamics of the nonlinear DPSs. A two-step solving approach was further developed to learn the model. Additional analysis and proof of concept showed the effectiveness of this proposed method. This proposed method is different from traditional data-driven modeling methods in that it uses full information from all sensors and does not require model reduction technology. Case studies not only demonstrate the effectiveness of this proposed method, but also its superior modeling performance as compared with several commonly used methods.

关键词： Sensors Spatiotemporal phenomena Mathematical model Graphical models Distribution functions Artificial neural networks distributed parameter systems neural network partial differential equation spatiotemporal modeling

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Delay-independent sliding mode control for a class of quasi-linear parabolic distributed parameter systems with time-varying delay

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2013年第2期350卷 397-418页

作者： Xing, Hailong Li, Donghai Gao, Cunchen Kao, Yonggui Qingdao Agr Univ Sci & Informat Coll Qingdao 266109 Peoples R China Tsinghua Univ Dept Thermal Engn State Key Lab Power Syst Beijing 100084 Peoples R China Ocean Univ China Sch Math Sci Qingdao 266100 Peoples R China Harbin Inst Technol Sch Sci Weihai 264200 Peoples R China

The sliding mode control (SMC) problem for a class of quasi-linear parabolic partial differential equation (PDE) systems with time-varying delay is considered. Firstly, the stability problem for the reduced order sliding dynamical equations is investigated and a sufficient condition for the stability of sliding motion is given. Then the SMC law, which forces the system state from any initial state to reach the sliding manifold within finite time, is designed. At last a simulation example is presented to illustrate effectiveness of the proposed method. Crown Copyright (C) 2012 Published by Elsevier Ltd. on behalf of The Franklin Institute All rights reserved.

关键词： SLIDING mode control QUASILINEARIZATION distributed parameter systems TIME-varying systems TIME delay systems PARTIAL differential equations STABILITY theory SIMULATION methods & models

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Feedback control for a class of semi-linear parabolic distributed parameter systems with mixed time delays

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INTERNATIONAL JOURNAL OF systems SCIENCE 2020年第4期51卷 585-600页

作者： Ji, Huihui Zhang, He Cui, Baotong Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Sch Internet Things Engn Wuxi 214122 Jiangsu Peoples R China Nanjing Univ Sci & Technol Sch Automat Nanjing Peoples R China

This paper investigates the design problem of collocated feedback controllers for a class of semi-linear distributed parameter systems with mixed time delays. The spatially distributed is divided by a finite number of intermittently local actuators and sensors. In order to deal with the problem of exponential stability analysis, the framework of a class of novel interval Lyapunov functional is established. By utilising Schur complement and linear matrix inequality (LMI) techniques, the corresponding stabilisation condition is then derived. Furthermore, the robust control problem is considered for the uncertain distributed parameter systems with external load disturbance and mixed time delays. Based on the feedback controller, the exponentially stability condition is derived for the uncertain systems. Finally, the simulation examples are presented to show the effectiveness of the proposed feedback control approach for Fisher equation and Blake-Scholes option pricing model.

关键词： distributed parameter systems exponential stability mixed time delays collocated actuators and sensors H-infinity exponentially stability

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Event-driven observer-based control for distributed parameter systems using mobile sensor and actuator

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2016年第12期72卷 2854-2864页

作者： Jiang, Zhengxian Cui, Baotong Wu, Wei Zhuang, Bo Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Sch IoT Engn Wuxi 214122 Peoples R China Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China

This paper considers the event-driven observer-based control for distributed parameter systems using mobile sensor and actuator. An observer is designed to estimate the states of the distributed parameter systems based on the measurement information provided by the mobile sensor. In order to reduce the frequency of the signal transmissions between the observer and the controller, an event-driven scheme is introduced. Once an event is generated, the event detector will send the newest observer state to the controller. Meanwhile, a guidance scheme is provided to drive the actuator to the position where the observer state reaches the maximum value to improve the control performance. For the event-driven control system, the global uniform ultimate boundedness can be guaranteed by the Lyapunov functional approach despite the reduced sampling frequency. A numerical example is finally presented to illustrate the effectiveness and the advantages of the proposed approaches. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Event-driven Observer distributed parameter systems Mobile sensor Mobile actuator

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Exponential stability of linear distributed parameter systems with time-varying delays

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AUTOMATICA 2009年第1期45卷 194-201页

作者： Fridman, Emilia Orlov, Yury Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel CICESE Res Ctr Ensenada 22860 Baja California Mexico

Exponential stability analysis via the Lyapunov-Krasovskii method is extended to linear time-delay systems in a Hilbert space. The operator acting on the delayed state is supposed to be bounded. The system delay is admitted to be unknown and time-varying with an a priori given upper bound on the delay. Sufficient delay-dependent conditions for exponential stability are derived in the form of Linear Operator Inequalities (LOIs), where the decision variables are operators in the Hilbert space. Being applied to a heat equation and to a wave equation, these conditions are reduced to standard Linear Matrix Inequalities (LMIs). The proposed method is expected to provide effective tools for stability analysis and control synthesis of distributed parameter systems. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Time-varying delay Stability Lyapunov method LMI

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ASYMPTOTIC STABILITY OF distributed parameter systems WITH FEEDBACK CONTROLS

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1966年第1期AC11卷 46-+页

作者： WANG, PKC Department of Electrical Engineering University of Southern California Los Angeles CA USA

In this paper, the problem of stability in distributed parameter systems with feedback controls is formulated directly in the framework of partial differential equations without resorting to further approximations. Sufficient conditions for Lyapunov asymptotic stability are derived for particular classes of systems with distributed, mixed distributed, and boundary control laws, and also for systems with time delay. The applications of the main results are illustrated by examples.

关键词： Asymptotic stability distributed parameter systems Feedback control Partial differential equations Mathematical model Control systems Adaptive control Stress Sufficient conditions distributed control

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FINITE-DIMENSIONAL ADAPTIVE OBSERVERS APPLIED TO distributed-parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1993年第3期38卷 469-474页

作者： LILLY, JH Department of Electrical Engineering Speed Scientific School University of Louisville Louisville KY USA

The application of finite-dimensional adaptive observers to distributed parameter systems is addressed. Ultimate boundedness of the parameter and state errors are proven in the case of residuals which have finite energy over a finite time interval, provided the plant input is definitely exciting. In the absence of definite excitation, an error growth rate proportional to t1/2 is proven. The results are obtained without assuming plant stability or input boundedness.

关键词： distributed parameter systems Observers State estimation Read only memory Adaptive control parameter estimation Stability Programmable control State feedback Reduced order systems

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Disturbance rejection in a class of adaptive control laws for distributed parameter systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2009年第2期23卷 166-192页

作者： Kim, Rin Y. Bentsman, Joseph Univ Illinois Dept Mech Sci & Engn Urbana IL 61801 USA

A recently introduced class of the well-posed error systems and the corresponding robust model reference adaptive control laws for the systems represented by the parabolic or the hyperbolic partial differential equations (PDEs) with the spatially varying parameters and a distributed sensing and actuation is extended to encompass the disturbance rejection capability. The disturbance is modeled as a space-time-varying signal generated by a parabolic PDE with the known parameters, a spatially varying time-invariant signal, and a space-time-varying signal with the known time variation. The case of the time-invariant disturbance model is shown to lead to a distributed adaptive PI control law, thereby making a well-posed connection to the classical finite-dimensional control structures. The numerical simulations indicate that the control laws proposed are robust with respect to the plant/reference model as well as the disturbance/disturbance observer mismatch in the boundary conditions. Copyright (c) 2008 John Wiley & Sons, Ltd.

关键词： adaptive control distributed parameter systems disturbance rejection

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