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Chinese Control Conference (CCC)

作者： Yahui Sun Zhaoqiang Ge Xi'an Jiaotong University Xi'an Shaanxi CN

This paper discusses the existence and uniqueness of strong solutions for the first order homogeneous linear generalized distributed parameter system and nonhomogeneous linear generalized distributed parameter system by using the generalized operator semigroup theory. And sufficient conditions of existence and uniqueness of strong solutions and constructive expressions of strong solutions are given in the paper. Further, the existence of strong solutions of semilinear generalized distributed parameter system is studied by mild solutions.

关键词： distributed parameter systems Hilbert space Generators Time-varying systems Gold Educational institutions

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A Kalman Filtering Approach for Detection of Option Mispricing in the Black-Scholes PDE Model

A Kalman Filtering Approach for Detection of Option Misprici...

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IEEE Conference on Computational Intelligence for Financial Engineering and Economics (CIFEr)

作者： Rigatos, Gerasimos Ind Syst Inst Unit Ind Automat Rion 26504 Greece

ISBN: (纸本)9781479923809

The paper considers financial derivatives and option pricing models which are described with the use of diffusion-type partial differential equations (e.g. Black-Scholes models). Using this approach a new filtering method for distributed parameter systems is developed, for estimating option prices variations without knowledge of initial conditions. The proposed filtering method is the so-called Derivative-free nonlinear Kalman Filter and is based on a decomposition of the nonlinear partial-differential equation of the financial system into a set of ordinary differential equations with respect to time. Next, each one of the local models associated with the ordinary differential equations is written in the linear canonical form through a transformation which is based on differential flatness theory. This transformation provides a model of the nonlinear dynamics of the option pricing model for which state estimation is possible by applying the standard Kalman Filter recursion. Based on the obtained state estimate, validation of the Black-Scholes PDE model can be performed and the existence of inconsistent parameters in the Black-Scholes PDE model can be concluded.

关键词： Indexes Kalmanfilters Mathematicalmodel Numericalmodels Partialdifferentialequations Pricing Security Pricing Ordinary differential equation Security Partial differential equations Canonical form State estimation distributed parameter systems Kalman filtering Nonlinear Dynamics Kalman filters

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Spatio-temporal responses of a class of 2 x 2 hyperbolic systems 19

Spatio-temporal responses of a class of 2 x 2 hyperbolic sys...

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19th International Conference on Methods and Models in Automation and Robotics (MMAR)

作者： Bartecki, Krzysztof Opole Univ Technol Inst Control & Comp Engn PL-45272 Opole Poland

ISBN: (纸本)9781479950812

Results of the spatio-temporal analysis of a class of distributed parameter systems described by hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of the two boundary inputs of Dirichlet type applied at the same point of the spatial domain, the analytical expressions for the impulse response functions are derived based on the inverse Laplace transform of individual elements of the 2 x 2 transfer function matrix. The considerations are illustrated with a practical example of a coaxial heat exchanger operating in parallel-flow mode which correspond to the analyzed boundary conditions.

关键词： Laplace transforms control system analysis distributed control hyperbolic equations matrix algebra partial differential equations Dirichlet type boundary inputs boundary conditions coaxial heat exchanger distributed parameter systems hyperbolic partial differential equations hyperbolic systems inverse Laplace transform one-dimensional spatial domain parallel-flow mode spatio-temporal analysis spatio-temporal response transfer function matrix Boundary conditions Equations Laplace equations Resistance heating Transfer functions Transmission line matrix methods transmission line matrix methods inverse Laplace transform hyperbolic systems distributed parameter systems Boundary conditions Resistance heating Laplace's equation Laplace transform Control system analysis TRANSFER FUNCTIONS hyperbolic equations Differential equations matrix algebra decentralised control Spatio-Temporal Analysis

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Finite Volume and Finite Element Models for Real-Time Control and State Estimation of Two-Dimensional Heat Transfer Processes 19

Finite Volume and Finite Element Models for Real-Time Contro...

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19th International Conference on Methods and Models in Automation and Robotics (MMAR)

作者： Rauh, Andreas Senkel, Luise Aschemann, Harald Univ Rostock Chair Mechatron D-18059 Rostock Germany

ISBN: (纸本)9781479950812

Control design for distributed parameter systems usually makes use of either finite volume or finite element approximations of the governing partial differential equations (PDEs). The aim of using both finite volume and finite element models is to obtain a finite-dimensional state-space representation of the dynamics which can be used directly for the design of feedback or feedforward controllers as well as state observers. However, finite volume models only provide a coarse description of flow and storage variables since these are assumed to be piecewise homogeneous in the corresponding volume elements. In contrast, finite element models exploit parameterizable ansatz functions such as polynomials for each element so that smooth representations of the before-mentioned quantities become possible. However, classical finite element techniques do not provide reliable measures for the quantification of the achievable approximation quality. This drawback is removed by the method of integrodifferential relations (MIDR). Simulations and experiments for the observer-based control of a spatially two-dimensional heat transfer process with distributed control inputs are presented in this paper to visualize differences between finite element models relying on the MIDR and finite volume representations.

关键词： control system synthesis distributed parameter systems feedback feedforward finite element analysis finite volume methods heat transfer integro-differential equations observers partial differential equations state-space methods MIDR PDE control design control estimation distributed control inputs feedback controller feedforward controller finite element model finite volume model finite-dimensional state-space representation flow variables integrodifferential relations observer-based control parameterizable ansatz functions state estimation state observers storage variables two-dimensional heat transfer process Approximation methods Eigenvalues and eigenfunctions Finite element analysis Heat transfer Heating Polynomials Vectors

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KPCA-ARX time-space modeling for distributed parameter system*

KPCA-ARX time-space modeling for distributed parameter syste...

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Chinese Control and Decision Conference, CCDC

作者： Jingjing Yang Jili Tao Ningbo Institute of Technology Zhejiang University 315100 China

Modeling of distributed parameter systems (DPSs) is difficult because of their infinite dimensional time-space nature. For a class of nonlinear distributed parameter systems described by parabolic partial differential equations (PDEs), Kernel Principal Component Analysis (KPCA) method is utilized to extract the nonlinear basis functions in dominant space, and the time-space decomposition is carried out in terms of these basis functions to obtain the outputs in time domain. Since the dominant space extraction is influenced by the parameters of kernel functions, they are optimized by Genetic Algorithm (GA) to obtain more system information with less principal components. The input stimulation and time domain outputs are used to construct the ARX model, which is identified by the recursive least squares algorithm. The simulation results show that the proposed method can obtain more system information with less principal components and gain satisfying reconstruction accuracy.

关键词： Principal component analysis Mathematical model Kernel distributed parameter systems Eigenvalues and eigenfunctions Computational modeling Optimization

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A Lyapunov Approach to Second-Order Sliding-Mode Boundary Control of an Unstable Heat System with Spatiotemporal-Varying parameters under Boundary Disturbances

A Lyapunov Approach to Second-Order Sliding-Mode Boundary Co...

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American Control Conference

作者： Cheng, Meng-Bi Su, Wu-Chung Radisavljevic-Gajic, Verica Oezguner, Uemit Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

ISBN: (纸本)9781479932740

This paper considers a boundary stabilization problem of an unstable heat system incorporated with spatial and temporal varying coefficients subjected to boundary uncertainties. The system model is governed by a second-order parabolic partial differential equation (PDE). By taking the Volterra integral transformation, we can obtain a target PDE with asymptotic stability characteristics in the new coordinates when an appropriate backstepping boundary control input is applied. The implicated backsteeping control law can be further integrated into the matched boundary disturbance. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance. Based on the Lyapunov method, a second-order sliding-mode boundary control, constructed by the integration of discontinuous signal, is employed to maintain the robustness to matched boundary disturbance. The closed-loop stability of the controlled system is also verified. Simulation results are provided to demonstrate the feasibility of this proposed control scheme.

关键词： Boundary control distributed parameter systems partial differential equations sliding-mode control

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distributed Attitude Coordinated Tracking Control for Multi-group Spacecrafts Based On Input Normalized Adaptive Neural Network

Distributed Attitude Coordinated Tracking Control for Multi-...

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American Control Conference

作者： Liu, Xiangdong Gan, Chao Lu, Pingli BIT Sch Automat Beijing Peoples R China

ISBN: (纸本)9781479932740

In this paper, the distributed attitude coordinated tracking controller is presented for multi-group spacecrafts based on input normalized adaptive neural network. In contrast to the existing works about spacecraft formation flying(SFF), where all spacecrafts reach the same reference attitude asymptotically, we require that all spacecrafts track several leaders and each spacecraft only synchronize within its group leader, respectively. A distributed finite time observer is proposed for each spacecraft to obtain an accurate estimation of its corresponding reference attitude. A distributed attitude coordination controller based on input normalized neural network is proposed to guarantee that the whole spacecrafts track their corresponding reference attitude cooperatively. Based on Lyapunov theory, the stability of the overall closed-loop system is guaranteed, and numerical simulations are shown to demonstrate the effectiveness of the proposed controller.

关键词： Attitude control Neural networks Observers Space vehicles Uncertainty Vectors distributed parameter systems Estimation

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Vibration Control Design for a Flexible String with Input Saturation 11

Vibration Control Design for a Flexible String with Input Sa...

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11th World Congress on Intelligent Control and Automation

作者： He, Wei Sun, Chen Ge, Shuzhi Sam Univ Elect Sci & Technol China Inst Robot Chengdu 611731 Peoples R China Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

ISBN: (纸本)9781479958252

In this paper, we consider the vibration control problem of a flexible string system in the presence of input saturation. The dynamics of the string system are represented by the coupled partial differential equation (PDE) and ordinary differential equation (ODE). In order to suppress the transverse vibration of the flexible string system, boundary control is proposed by introducing a well-defined integral Lyapunov function. An auxiliary system is introduced to handle the effect of input saturation, and the proof for the existence and the uniqueness of the solution of the closed-loop system is presented. The exponential stability is achieved through rigorous analysis without any simplification of the dynamics. The results are illustrated with numerical simulations for verifying the control performance.

关键词： Vibration control Input saturation distributed parameter systems Boundary control Flexible structure

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Special Issue: Adaptive Identification and Control of distributed parameter systems (DPS)

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2009年第2期23卷 111-113页

作者： Bentsman, Joseph Orlov, Yuri Univ Illinois Dept Mech Sci & Engn Urbana IL 61801 USA CICESE Res Ctr Elect & Telecommun Dept Ensenada Baja California Mexico

This special issue contains the revised and updated versions of the papers presented in the session oil adaptive identification and control held at the 45th IEEE Control and Decision Conference in Sail Diego, CA, oil December 12-15, 2006, co-organized and co-chaired by Joseph Bentsman and Miroslav Krstic. Covering stochastic modeling and identification, adaptive identification and control, and automated fault detection for distributed parameter systems governed by partial differential and functional equations, the papers provide a coherent selection of novel results in the area.

关键词： adaptive identification adaptive control distributed parameter systems parameter estimation automated fault detection disturbance rejection saptiotemporal noise

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Sliding Mode Boundary Control for an Euler-Bernoulli Beam with Boundary Disturbances and parameter Variations

Sliding Mode Boundary Control for an Euler-Bernoulli Beam wi...

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American Control Conference

作者： Karagiannis, Dimitri Radisavlejevic-Gajic, Verica Villanova Univ Dept Mech Engn Ctr Nonlinear Dynam & Control CENDAC Villanova PA 19085 USA

ISBN: (纸本)9781479932740

This work addresses the problem of stability and control of an Euler-Bernoulli beam with sliding-pinned boundary conditions. The control comes in the form of an applied displacement and bending moment on the pinned end. The proposed controller accounts for bounded exogenous disturbances on the pinned end boundary conditions, representing a number of possible practical issues such as model parameter uncertainties or unknown external forces. This controller takes advantage of a technique for stabilizing an Euler-Bernoulli beam through a Schrodinger equation representation and a previously developed integral transformation which provides the opportunity to select arbitrary damping for the system. The contribution of this work is to introduce unknown boundary disturbances into the system boundary terms and the development of a Sliding Mode Controller which effectively drives the system states to an exponentially stable infinite-dimensional sliding surface which then eliminates the system vibration with arbitrary damping. The resulting control efforts developed are continuous functions and therefore do not create a chattering effect on control actuators.

关键词： Boundary conditions Equations Integral equations Kernel Mathematical model Transforms Uncertainty distributed parameter systems Flexible structures Variable-structure/sliding-mode control

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