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Optimization of boundary and starting controls in multi-dimensional hyperbolic systems

IFAC Proceedings Volumes 1999年第2期32卷 2803-2806页

作者： Alexander V. Arguchintsev Irkutsk State University Mathematical Department 1 K.Marx Street Irkatsk 664003 Russia.

An optimization problem of initial-boundary conditions for first-order multi-dimensional semiiincar hyperbolic systems is considered in this paper. The special feature of the general optimization problem for boundary conditions is non-validity uf the classic optimality condition of Pontryagin's type. The idea of special 'inner' variations of admissible smooth controls is used For deriving a new optimality condition. The numerical algorithm based on the optimality condition is given. Some possible applications are discussed

关键词： Optimal control distributed-parameter systems optimally convergence of numerical methods

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FREE BEAM VIBRATION ANALYSIS BASED ON THE METHOD OF INTEGRODIFFERENTIAL RELATIONS

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IFAC Proceedings Volumes 2007年第14期40卷 115-119页

作者： V.V. Saurin G.V. Kostin Institute for Problems in Mechanics of the Russian Academy of Sciences

Equations describing small free oscillations of a rectilinear elastic beam with a rectangular cross section have been obtained within the framework of the linear theory of elasticity and solved using the method of integrodifferential relations (IDR). The influence of geometry and elastic characteristics on the frequencies and shapes of free beam oscillations is studied. It is shown that the longitudinal motions admit two types of displacement and internal stress fields. The lateral oscillations obtained are specified by two frequency bands, which correspond to different types of the characteristic equation roots. Numerical examples of free beam oscillations are presented and discussed. Copyright © 2002 IFAC

关键词： distributed-parameter systems Eigenvalue problems Frequency characteristics Verification

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ON OPTIMIZATION OF HYPERBOLIC systems WITH SMOOTH CONTROLS AND INTEGRAL CONSTRAINTS

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IFAC Proceedings Volumes 2002年第1期35卷 323-327页

作者： Alexander V. Arguchintsev Irkutsk State University 1 K.Marx Street Irkutsk 664003. Russia

A non-classic optimality condition and numerical algorithm for smooth boundary controls in semi-linear first-order hyperbolic systems are presented. Additional integral control constraints are considered. The suggested approach is based on special variations of admissible continuously differentiable controls. These variations lead to a new necessary optimality condition which is a base for a numerical method. The method is applied to an optimal control problem for an age-structured population.

关键词： Optimal control partial differential equations distributed-parameter systems boundary conditions computational methods

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FINITE-DIMENSIONAL CONTROLLER DESIGN FOR NONLINEAR EVOLUTION EQUATIONS USING INERTIAL FORMS

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IFAC Proceedings Volumes 2005年第1期38卷 235-239页

作者： D. Coca Department of Automatic Control & Systems Engineering University of Sheffield Mappin Street Sheffield S1 3JD UK

This article deals with the problem of designing finite dimensional controllers for a class of nonlinear infinite dimensional systems for which inertial manifolds are known to exist. The synthesis of the controller is based on a finite-dimensional, inertial form approximation of the plant. The controller guarantees exponential convergence of the system state to zero.

关键词： Partial differential equations distributed-parameter systems Nonlinear systems Exponentially stable

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Optimal Boundary Control of Kuramoto-Sivashinsky Equation

Optimal Boundary Control of Kuramoto-Sivashinsky Equation

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2009 American Control Conference (ACC 2009)

作者： Stevan Dubljevic Department of Chemical and Biomolecular Engineering University of California Los Angeles CA 90095

ISBN: (纸本)9781424445233

This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Kuramoto-Sivashinsky Equation Boundary control LQR State/Output Feedback Control

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Design and Experimental Validation of an Output Feedback Controller for a Pneumatic System with distributed parameters

Design and Experimental Validation of an Output Feedback Con...

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International Conference on Control, Automation and systems

作者： R. Kern N. Gehring J. Deutscher M. Meissner Chair of Automatic Control Technical University of Munich Garching Germany Institute of Automatic Control and Control Systems Technology Johannes Kepler University Linz Austria Chair of Automatic Control Friedrich-Alexander University Erlangen-Nurnberg Erlangen Germany

ISBN: (纸本)9781538670804;9788993215168

This paper considers the model-based control of a pneumatic system, where a tank is connected to a valve via a long tube. Due to the significant distance between the control input and the pressure in the tank to be controlled, a distributed-parameter model is used for the tube, involving quasilinear hyperbolic partial differential equations. In contrast, the tank is modelled by ordinary differential equations. Experimental data verifies the validity of the corresponding quasilinear system model. Based on a less accurate, linear PDE-ODE system model, derived there upon, both, a back-stepping controller and a backstepping observer are designed. The resulting output feedback controller is augmented by a flatness-based feedforward controller. Experimental results for tube lengths of approximately five and twenty meters show that this controller allows to track fast pressure changes in the tank almost perfectly.

关键词： Pneumatic systems distributed-parameter systems Partial differential equations Model-based control Feed-back control Observer Backstepping Experimental validation

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Discrete mechanics optimal control (DMOC) and model predictive control (MPC) synthesis for reaction-diffusion process system with moving actuator

Discrete mechanics optimal control (DMOC) and model predicti...

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American Control Conference

作者： Stevan Dubljevic Marin Kobilarov James Ng Chemical & Materials Engineering Department University of Alberta AB T6G 2V4 Canada Control and Dynamics Systems California Institute of Technology Pasadena CA 91125 USA

ISBN: (纸本)9781424474264

This paper is concerned with the computation of optimal motion control as well as the optimal input injection policy of an actuator arm regulating the temperature in a reaction-diffusion system. The system has two dynamical components consisting of the arm mechanics with inertial, elastic and damping properties, which is driven by bounded mechanical actuation controls and an underlying reaction-diffusion system described by the parabolic PDE. The state of the actuator arm parametrizes the input injection operator of the parabolic PDE systems model and causes coupling between the two dynamical systems generally operating at different time scales. The method proposed in this paper is aimed at solving this coupled problem. The actuator mechanics and its control are achieved in the discrete mechanics and optimal control (DMOC) framework, while the input injection for the reaction diffusion system is calculated by the modal model predictive control (MMPC) algorithm suitable for the dissipative systems. The actuation arm policy and input to the parabolic PDE system include in its realization low-order discrete representation of the parabolic PDE evolution and incorporate optimality with respect to both the state of the PDE and the actuator displacement cost from current to some more optimal control position as well as naturally present input and PDE state constraints. The proposed actuation arm policy and optimal stabilization of the unstable reaction-diffusion system in the presence of constraints in the full state-feedback controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Moving Actuator Discrete Mechanics Optimal Control (DMOC) Model Predictive Control (MPC) Input/State Constraints

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distributed Finite Element Kalman Filter

Distributed Finite Element Kalman Filter

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European Control Conference

作者： G. Battistelli L. Chisci N. Forti G. Pelosi S. Selleri Dipartimento di Ingegneria dell'Informazione Universita degli Studi di Firenze

ISBN: (纸本)9781467371605

This paper addresses state estimation for spatially distributed systems governed by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. A decentralised and scalable approach is undertaken by decomposing the domain into overlapping subdomains assigned to different processing nodes interconnected to form a network. Each node runs a local finite-dimensional Kalman filter which exploits the finite element approach for spatial discretisation and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains. The effectiveness of the proposed distributed consensus-based finite element Kalman filter is demonstrated via simulation experiments concerning a temperature estimation problem modelled by the bidimensional heat equation.

关键词： Networked state estimation distributed-parameter systems Finite element method Kalman filtering Consensus

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Boundary Model Predictive Control of Kuramoto-Sivashinsky Equation with Input and Point State Constraints

Boundary Model Predictive Control of Kuramoto-Sivashinsky Eq...

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Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference

作者： Stevan Dubljevic Department of Chemical and Materials Engineering University of Alberta

In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation(KSE) is been utilized in the model modal predictive control(MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state *** KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation(PDE).An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller(MMPC) incorporating both the pointwise enforced KSE state constraints and input *** proposed control problem formulation and the performance of the closed-loop system in the full statefeedback controller realization have been evaluated through simulations.

关键词： distributed-parameter systems Kuramoto Sivashinsky Equation Boundary Control Model Predictive Control(MPC) Input/State Constraints

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Sliding Mode Boundary Control of Unstable Parabolic PDE systems with parameter Variations and Matched Disturbances

Sliding Mode Boundary Control of Unstable Parabolic PDE Syst...

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2009 American Control Conference (ACC 2009)

作者： Meng-Bi Cheng Verica Radisavljevic Wu-Chung Su Electrical Engineering Department at National Chung Hsing University Taiwan Electrical and Computer Engineering Department at Rutgers State University of New Jersey

ISBN: (纸本)9781424445233

This paper considers the stabilization problem of a one-dimensional unstable heat conduction system subject to parametric variations and boundary uncertainties. This system is modeled as a parabolic partial differential equation (PDE) and is only powered from one boundary with a Dirichlet type of actuator. By taking the Volterra integral transformation, we obtain a nominal PDE with asymptotic stability characteristics in the new coordinates when an appropriate boundary control input is applied. 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, and is robust against certain types of parameter variations. A continuous variable structure boundary control law is employed to attain the sliding mode on the sliding surface. The proposed method can be extended to other parabolic PDE systems such as diffusion-advection system. Simulation results are demonstrated and compared with the other outstanding back-stepping control schemes.

关键词： Boundary control chattering distributed-parameter systems sliding surface Lyapunov methods parameter variation Sliding mode Boundary boundary layer Liapunov function Slip surfaces Unstable actuators heat conduction system

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