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Nonlinear observer for distributed parameter systems described by decoupled advection equations

JOURNAL OF VIBRATION AND CONTROL 2017年第7期23卷 1152-1165页

作者： Kamran, Niloofar N. Drakunov, Sergey V. Solano, Wanda M. Embry Riddle Aeronaut Univ Dept Phys Sci 600 South Clyde Morris Blvd Daytona Beach FL 32114 USA

In this paper a nonlinear observer for a class of partial differential equations known as the advection equation is designed. The observer, that uses only boundary measurements, is developed based on the sliding mode method. The convergence of states of the observer to the actual system, in spite of possible mismatches between the model and the system, is proven through the Lyapunov stability techniques. In addition, a sliding mode method is employed to design an anomaly detection system that is able to identify parameters of the disturbance in the system such as intensity and location. The Lyapunov stability theorem has been used in order to guarantee the convergence of the anomaly detection system. The applications of observer and anomaly detector are illustrated through simulation.

关键词： Nonlinear observers distributed parameter systems advection equation sliding mode variable structure systems method of characteristics anomaly detection fluid flow in pipes leakage detection

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Event-generator-based H∞ control of fuzzy distributed parameter systems

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FUZZY SETS AND systems 2022年 432卷 28-49页

作者： Ji, Huihui Cui, Baotong Nanjing Audit Univ Sch Stat & Math 86 West Yushan Rd Nanjing 211815 Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Jiangsu Peoples R China Jiangnan Univ Sch IoT Engn Wuxi 214122 Jiangsu Peoples R China

This paper studies the adaptive event-based H-infinity control problem for a class of T-S fuzzy distributed parameter system with parameter uncertain and actuator faults. To overcome the drawback of the period control scheme, an event-triggered control scheme with adaptive threshold is proposed to minimize the number of unnecessary sampled data transmission and to reduce the update frequency of the controller. Furthermore, a T-S fuzzy controller based on the adaptive event-triggered sampled data is designed to ensure the stochastic exponential stability of the distributed parameter system with H-infinity disturbance attenuation performance. Based on a new Lyapunov functional and inequality technique, the stochastic exponential stability criterion of the closed-loop system is obtained, and the controller parameters are designed. The new developed inequality can reduce the conservatism of the stability criterion. Finally, the effectiveness of the theoretical calculation results is verified by numerical simulation, and the results are compared with the relevant literature in the simulation, showing that the methods and results in this paper are less conservative. (C) 2021 Elsevier B.V. All rights reserved.

关键词： distributed parameter systems Adaptive event-triggered control H-infinity control T-S fuzzy model Actuator fault Stochastic exponential stability

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OPTIMAL FILTERING ALGORITHM USING COVARIANCE INFORMATION IN LINEAR DISCRETE-TIME distributed-parameter systems

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SIGNAL PROCESSING 1993年第1期33卷 45-56页

作者： NAKAMORI, S Department of Technology Faculty Education Kagoshima University 1-20-6 Kohrimoto Kagoshima 890 Japan

This paper presents an optimal discrete-time filtering algorithm using covariance information in linear distributed parameter systems. It is assumed that observation noise is a white Gaussian process. The autocovariance function of the signal, the variance of white Gaussian noise and the observed value are used in the filtering algorithm. It is an advantage that the current filtering algorithm is applied to the case where a difference equation, which generates a signal process, is unknown in linear stochastic distributed parameter systems.

关键词： IMAGE RESTORATION LANDSAT IMAGE distributed parameter systems

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A TRANSFER-FUNCTION FORMULATION FOR NONUNIFORMITY distributed-parameter systems

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JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME 1994年第4期116卷 426-432页

作者： YANG, B FANG, H Department of Mechanical Engineering University of Southern California Los Angeles CA 90089-1453

This paper studies a transfer-function formulation for general one-dimensional, nonuniformly distributed systems, subject to arbitrary boundary conditions and external disturbances. In the development, the governing equations of the nonuniform system are cast into a state-space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state-space equation. Two approximate methods, the step-function approximation and truncated Taylor series, are proposed to evaluate the fundamental matrix. With the transfer-function formulation, various dynamics and control problems for the nonuniformly distributed system can be conveniently addressed. The transfer-function analysis also is applied to constrained/combined nonuniformly distributed systems. The method developed is illustrated on two non-uniform beams.

关键词： Dynamics (Mechanics) Laplace transforms distributed parameter systems Transfer functions Boundary-value problems Approximation

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A Galerkin/neural-network-based design of guaranteed cost control for nonlinear distributed parameter systems

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IEEE TRANSACTIONS ON NEURAL NETWORKS 2008年第5期19卷 795-807页

作者： Wu, Huai-Ning Li, Han-Xiong Beijing Univ Aeronaut & Astronaut Beihang Univ Sch Automat Sci & Elect Engn Beijing 100083 Peoples R China City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

This paper presents a Galerkin/neural-network-based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

关键词： distributed parameter systems Galerkin method guaranteed cost control (GCC) linear matrix inequality (LMI) neural network stability

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Low-order empirical modeling of distributed parameter systems using temporal and spatial eigenfunctions

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COMPUTERS & CHEMICAL ENGINEERING 2005年第4期29卷 817-827页

作者： Bleris, LG Kothare, MV Lehigh Univ Dept Chem Engn Integrated Microchem Syst Lab Bethlehem PA 18015 USA Lehigh Univ Dept Elect & Comp Engn Integrated Microchem Syst Lab Bethlehem PA 18015 USA

We provide a methodology for retrieving spatial and temporal eigenfunctions from an ensemble of data, using Proper Orthogonal Decomposition (POD). Focusing on a Newtonian fluid flow problem, we illustrate that the efficiency of these two families of eigenfunctions can be different when used in model reduction projections. The above observation can be of critical importance for low-order modeling of distributed parameter systems (DPS) in on-line control applications, due to the computational savings that are introduced. Additionally, for the particular fluid flow problem, we introduce the use of the entropy of the data ensemble as the criterion for choosing the appropriate eigenfunction family. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： empirical modeling distributed parameter systems eigenfunctions

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distributed proportional plus second-order spatial derivative control for distributed parameter systems subject to spatiotemporal uncertainties

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NONLINEAR DYNAMICS 2014年第4期76卷 2041-2058页

作者： Wang, Jun-Wei Li, Han-Xiong Wu, Huai-Ning Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Kowloon Hong Kong Peoples R China Cent South Univ State Key Lab High Performance Complex Mfg Changsha Hunan Peoples R China Beijing Univ Aeronaut & Astronaut Sch Automat Sci & Elect Engn Sci & Technol Aircraft Control Lab Beihang Univ Beijing 100191 Peoples R China

In this paper, a robust distributed control design based on proportional plus second-order spatial derivative (P-sD) is proposed for exponential stabilization and minimization of spatial variation of a class of distributed parameter systems (DPSs) with spatiotemporal uncertainties, whose model is represented by parabolic partial differential equations with spatially varying coefficients. Based on the Lyapunov's direct method, a robust distributed P-sD controller is developed to not only exponentially stabilize the DPS for all admissible spatiotemporal uncertainties but also minimize the spatial variation of the process. The outcome of the robust distributed P-sD control problem is formulated as a spatial differential bilinear matrix inequality (SDBMI) problem. A local optimization algorithm that the SDBMI is treated as a double spatial differential linear matrix inequality (SDLMI) is presented to solve this SDBMI problem. Furthermore, the SDLMI optimization problem can be approximately solved via the finite difference method and the existing convex optimization techniques. Finally, the proposed design method is successfully applied to feedback control problem of the FitzHugh-Nagumo equation.

关键词： distributed parameter systems Robust control Exponential stability Spatiotemporal uncertainty Linear matrix inequalities (LMIs)

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Nonlinear model predictive control for distributed parameter systems using data driven artificial neural network models

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COMPUTERS & CHEMICAL ENGINEERING 2008年第6期32卷 1225-1237页

作者： Aggelogiannaki, Eleni Sarimveis, Haralambos NTUA Sch Chem Engn Athens 15780 Greece

In this work the radial basis function neural network architecture is used to model the dynamics of distributed parameter systems (DPSs). Two pure data driving schemes which do not require knowledge of the governing equations are described and compared. In the first method, the neural network methodology generates the full model of the system that is able to predict the process outputs at any spatial point. Past values of the Process inputs and the coordinates of the specific location provide the input information to the model. The second method uses empirical basis functions produced by the Singular Value Decomposition (SVD) on the snapshot matrix to describe the spatial behavior of the system, while the neural network model is used to estimate only the temporal coefficients. The models produced by both methods are then implemented in Model Predictive Control (MPC) coil figurations, suitable for constrained DPSs. The accuracies of the modeling methodologies and the efficiencies of the proposed MPC formulations are tested in a tubular reactor and produce encouraging results. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems radial basis function neural networks singular value decomposition model predictive control

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Iterative learning control for linear parabolic distributed parameter systems with multiple point sensors

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OPTIMAL CONTROL APPLICATIONS & METHODS 2023年第3期44卷 1174-1184页

作者： Liu, Yaqiang Lai, Jialun Jin, Zengwang Ren, Zhigang Xie, Shengli Wang, Yalin Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Guangdong Univ Technol Key Lab Intelligent Detect & Internet Things Mfg Minist Educ Guangzhou Peoples R China Northwestern Polytech Univ Sch Cybersecur Xian Peoples R China Guangdong Univ Technol Guangdong Key Lab IoT Informat Technol Guangzhou 510006 Peoples R China Guangdong Univ Technol Guangdong HongKong Macao Joint Lab Smart Discret Guangzhou Peoples R China Cent South Univ Sch Automat Changsha Peoples R China

This article presents an iterative learning control (ILC) approach for linear parabolic distributed parameter systems with multiple actuators and multiple sensors. The distribution functions of actuators and sensors are chosen as delta function to produce pointwise control and pointwise measurement. A P-type ILC law is proposed based on the iterative inputs and outputs to ensure the iterative process of the system is convergent under the ILC law. By utilizing integration by parts, triangle inequality, property of delta function, and Gronwall lemma, a sufficient condition based on an inequality constraint for the convergence analysis of the track error system is presented. Finally, the effectiveness of the proposed design method is verified by numerical simulation results.

关键词： convergence analysis distributed parameter systems iterative learning control pointwise measurement

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Robust control and tuning problem for distributed parameter systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 1996年第5期6卷 479-500页

作者： Hamalainen, T Pohjolainen, S Department of Mathematics Tampere University of Technology PO. Box 692 FIN-33101 Tampere Finland

In this paper robust multivariable controllers for parabolic distributed parameter systems will be discussed. The purpose of a robust controller is to achieve output regulation, disturbance rejection and insensitivity against some perturbations in the system's and controller's parameters. The robust controller consists of two parts: the unstable servo-compensator and the stabilizing compensator. The servo-compensator will be fixed on the basis of the spectrum of the reference and disturbance signals. The purpose of the stabilizing compensator is to stabilize the extended unstable system that consists of the stable plant and the servo-compensator. In this paper it is proved that the stabilizing compensator can be decomposed into a scalar gain and a matrix gain. A simple sufficient condition for finding stabilizing matrix gains will be given and a straightforward way to compute the gains will be presented. The proposed method is practical in the sense that the dimension of the controller is finite and small, output feedback is used and tuning the controller can be done with the information that can be measured from the stable plant with input-output measurements. To the authors' knowledge, the main results are new even for finite-dimensional systems.

关键词： robust control distributed parameter systems holomorphic semigroups tuning of low order controllers

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