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Flatness of Semilinear Parabolic PDEs-A Generalized Cauchy-Kowalevski Approach

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第9期58卷 2277-2291页

作者： Schoerkhuber, Birgit Meurer, Thomas Juengel, Ansgar Vienna Univ Technol Inst Anal & Sci Comp A-1040 Vienna Austria Univ Kiel Chair Automat Control D-24143 Kiel Germany

A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled semilinear systems of partial differential equations (PDEs) in a one-dimensional spatial domain. For this, the ansatz presented in "Trajectory planning for boundary controlled parabolic PDEs with varying parameters on higher-dimensional spatial domains" (T. Meurer and A. Kugi, IEEE Trans. Autom. Control, vol. 54, no, 8, pp. 1854-1868, Aug. 2009) using formal integration is generalized towards a unified design framework, which covers linear and semilinear PDEs including rather broad classes of nonlinearities arising in applications. In addition, an efficient semi-numerical solution of the implicit state and input parametrizations is developed and evaluated in different scenarios. Simulation results for various types of nonlinearities and a tubular reactor model described by a system of semilinear reaction-diffusion-convection equations illustrate the applicability of the proposed method.

关键词： distributed parameter systems flatness nonlinear control systems partial differential equations (PDEs) trajectory planning tubular reactor

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Boundary Control Synthesis for a Lithium-Ion Battery Thermal Regulation Problem

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AICHE JOURNAL 2013年第10期59卷 3782-3796页

作者： Ng, James Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB Canada

The thermal regulation problem for a lithium ion (Li-ion) battery with boundary control actuation is considered. The model of the transient temperature dynamics of the battery is given by a nonhomogeneous parabolic partial differential equation (PDE) on a two-dimensional spatial domain which accounts for the time-varying heat generation during the battery discharge cycle. The spatial domain is given as a disk with radial and angular coordinates which captures the nonradially symmetric heat-transfer phenomena due to the application of the control input along a portion of the spatial domain boundary. The Li-ion battery model is formulated within an appropriately defined infinite-dimensional function space setting which is suitable for spectral controller synthesis. The key challenges in the output feedback model-based controller design addressed in this work are: the dependence of the state on time-varying system parameters, the restriction of the input along a portion of the battery domain boundary, the observer-based optimal boundary control design where the separation principle is utilized to demonstrate the stability of the closed loop system, and the realization of the outback feedback control problem based on state measurement and interpolation of the temperature field. Numerical results for simulation case studies are presented. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3782-3796, 2013

关键词： Li-ion battery thermal regulation parabolic PDE distributed parameter systems nonautonomous systems boundary control observer design output feedback control

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Disturbance Rejection in 2 x 2 Linear Hyperbolic systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第5期58卷 1095-1106页

作者： Aamo, Ole Morten Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

Many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar. Typically, the disturbance occurs at the inlet of a pipeline or the bottom of an oil well, while sensing and actuation equipment is installed at the outlet, only, kilometers away from the disturbance. The present paper develops an output feedback control law for such cases, based on modelling the transport phenomenon as a 2 x 2 linear partial differential equation (PDE) of hyperbolic type and the disturbance as a finite-dimensional linear system affecting the left boundary of the PDE. Sensing and actuation are co-located at the right boundary of the PDE. The design provides a separation principle, allowing a disturbance attenuating full-state feedback control law to be combined with an observer. The results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations.

关键词： distributed parameter systems disturbance rejection fluid flow systems linear systems

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Reduced Order Internal Models in Robust Output Regulation

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第9期58卷 2307-2318页

作者： Paunonen, Lassi Pohjolainen, Seppo Tampere Univ Technol Dept Math FIN-33101 Tampere Finland

In this paper, we consider robust output regulation and the internal model principle for infinite-dimensional linear systems. We concentrate on a problem where the control law is required to be robust with respect to a restricted class of perturbations. We show that depending on the class of admissible perturbations, it is often possible to construct a robust controller with a smaller internal model than the one given by the internal model principle. In addition, we also look for minimal classes of perturbations that make the full internal model necessary. We introduce a straightforward way of testing for robustness of the control law for a given set of perturbations. The test in particular shows that the robustness is only dependent on the way the perturbations affect the transfer function of the plant at the frequencies of the exosystem. The theoretic results are applied to designing controllers for a one-dimensional wave equation and for a system consisting of three independent shock absorber models.

关键词： distributed parameter systems linear systems robust control

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CONTROLLING NONLINEAR INFINITE-DIMENSIONAL systems VIA THE INITIAL STATE

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2013年第5期51卷 3757-3780页

作者： Evans, Neil D. Univ Warwick Sch Engn Coventry CV4 7AL W Midlands England

A control problem is considered for nonlinear time-varying systems described by partial differential equations, in which the control acts only via part of the initial state. The problem is to drive part, or all, of the process to some desired state in a specified time. The motivation for such systems are control problems arising in medicine and biology that involve spatial or age characteristics, or time delays. The approach taken is to formulate the problem as a fixed point problem for a suitable abstract differential equation and then apply a version of the contraction mapping theorem. Conditions are imposed so that the problem is well defined and a weaker form of solution exists. The solution obtained ensures that the target state is achieved on the range of a linear operator arising from a linearisation of the system about an initial estimate for the control. Although the contraction mapping theorem yields a constructive method to determine the solution, an alternative, more direct, approach is presented, which relies on an iterative scheme for the control and the original dynamics.

关键词： distributed parameter systems initial state control fixed point theorems

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Adaptive distributed parameter and Input Estimation in Plasma Tokamak Heat Transport

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IFAC Proceedings Volumes 2013年第26期46卷 209-214页

作者： Sarah MECHHOUD Emmanuel WITRANT Luc DUGARD Didier MOREAU UJF-Grenoble 1/CNRS Grenoble Image Parole Signal Automatique (GIPSA-lab) UMR 5216 B.P. 46 F-38402 St Martin d'Hères France CEA IRFM F-13108 Saint Paul-Lez-Durance France

: In this paper, the adaptive estimation of spatially varying diffusion and source term coefficients for a linear parabolic partial differential equation describing tokamak plasma heat transport is considered. An estimator is defined in the infinite-dimensional framework having the system state and the parameters’ estimate as its states. Our scheme allows to estimate constant, spatially distributed and spatio-temporally distributed parameters as well as input with known upper bounds in time. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the Galerkin finite-dimensional technique is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.

关键词： Thermonuclear fusion distributed parameter systems input state and parameter estimation adaptive infinite-dimensional estimation Galerkin method

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H_∞ fuzzy observer-based control for a class of nonlinear distributed parameter systems with control constraints

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IEEE TRANSACTIONS ON FUZZY systems 2008年第2期16卷 502-516页

作者： Wu, Huai-Ning Li, Han-Xiong Beijing Univ Aeronaut & Astronaut 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

An H-infinity fuzzy observer-based control design is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems with control constraints, for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. In the proposed control scheme, Galerkin's method is initially applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T-S fuzzy model, a fuzzy observer-based controller is developed to stabilize the nonlinear PDE system and achieve an optimized H-infinity disturbance attenuation performance for the finite-dimensional slow system, while control constraints are respected. The outcome of the H-infinity fuzzy observer-based control problem is formulated as a bilinear matrix inequality (BMI) optimization problem. A local optimization algorithm that treats the BMI as a double linear matrix inequality is presented to solve this BMI optimization problem. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness.

关键词： bilinear matrix inequality (BMI) control constraints distributed parameter systems fuzzy control Galerkin's method H-infinity control

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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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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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Flatness-based and energy-based control for distributed parameter robotic systems

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IFAC Proceedings Volumes 2009年第4期42卷 1847-1852页

作者： Gerasimos G. Rigatos Spyros G. Tzafestas Unit of Industrial Automation Industrial Systems Institute Stadiou str. 26504 Rion Patras Greece Department of Electrical and Computer Engineering National Technical University of Athens Zografou 15773 Athens Greece

The paper presents a comparative study between flatness-based control and energy-based control when applied to flexible link robots. Flatness-based control is an open-loop nonlinear control method which is suitable for differentially flat systems i.e. systems the behavior of which is determined by a finite collection of quantities, consisting of the flat output and its derivatives. On the other hand energy-based control is a closed-loop control method, which unlike the absence of an explicit mathematical model of the flexible-link dynamics can succeed satisfactory performance of the associated control loop. The performance of flatness-based control is tested against energy-based control through simulation experiments.

关键词： flatness-based control energy-based control distributed parameter systems flexible-link robots trajectory tracking

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