Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems
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Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems
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Author : Martin Gugat
language : en
Publisher:
Release Date : 2015
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems written by Martin Gugat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems
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Author : Georges Bastin
language : en
Publisher: Birkhäuser
Release Date : 2018-04-22
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems written by Georges Bastin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-22 with Mathematics categories.
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.
Boundary Control And Variation
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Author : Jean-Paul Zolesio
language : en
Publisher: CRC Press
Release Date : 1994-07-28
Boundary Control And Variation written by Jean-Paul Zolesio and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-28 with Mathematics categories.
Based on the Working Conference on Boundary Control and Boundary Variation held in Sophia-Antipolis, France, this work provides important examinations of shape optimization and boundary control of hyperbolic systems, including free boundary problems and stabilization. It offers a new approach to large and nonlinear variation of the boundary using global Eulerian co-ordinates and intrinsic geometry.
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems
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Author : Martin Gugat
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Optimal Boundary Control And Boundary Stabilization Of Hyperbolic Systems written by Martin Gugat and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Science categories.
This brief considers recent results on optimal control and stabilization of systems governed by hyperbolic partial differential equations, specifically those in which the control action takes place at the boundary. The wave equation is used as a typical example of a linear system, through which the author explores initial boundary value problems, concepts of exact controllability, optimal exact control, and boundary stabilization. Nonlinear systems are also covered, with the Korteweg-de Vries and Burgers Equations serving as standard examples. To keep the presentation as accessible as possible, the author uses the case of a system with a state that is defined on a finite space interval, so that there are only two boundary points where the system can be controlled. Graduate and post-graduate students as well as researchers in the field will find this to be an accessible introduction to problems of optimal control and stabilization.
Boundary Control And Boundary Variations
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Author : J. P. Zolésio
language : en
Publisher: Springer
Release Date : 1988
Boundary Control And Boundary Variations written by J. P. Zolésio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This volume comprises the proceedings of the Working Conference "Boundary variations and boundary control" held in Nice (France), June 10-13, 1986. The aim of this Conference was to stimulate exchange of ideas between the group working on shape optimization (including free boundary problems) and the group working on boundary control of hyperbolic systems (including stabilization). An important remark is that if one considers a dynamical system governed by linear elasticity the choice of Lagrangian coordinates leads to discuss boundary conditions, or boundary control (for example to stabilize), while the choice of Eulerian coordinates lead to a moving boundary and moving domain . This remark challenges us to consider the domain (or its boundary) as a control.
Control Theory For Partial Differential Equations Volume 2 Abstract Hyperbolic Like Systems Over A Finite Time Horizon
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Author : Irena Lasiecka
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Control Theory For Partial Differential Equations Volume 2 Abstract Hyperbolic Like Systems Over A Finite Time Horizon written by Irena Lasiecka and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
Second of a two-volume treatise on deterministic control systems modeled by multi-dimensional partial differential equations.
Boundary Synchronization For Hyperbolic Systems
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Author : Tatsien Li
language : en
Publisher: Springer Nature
Release Date : 2019-12-02
Boundary Synchronization For Hyperbolic Systems written by Tatsien Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Science categories.
Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.
Structure Of Riccati Equation Solutions In Optimal Boundary Control Of Hyperbolic Equations With Quadratic Cost Functionals
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Author : Hock Lye Koh
language : en
Publisher:
Release Date : 1976
Structure Of Riccati Equation Solutions In Optimal Boundary Control Of Hyperbolic Equations With Quadratic Cost Functionals written by Hock Lye Koh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Calculus of variations categories.
This paper concerns the question of minimizing a quadratic cost functional associated with a linear symmetric hyperbolic control system over a finite time interval. A necessary and sufficient condition for a solution to exist is developed in terms of the solution of a two-point boundary value problem (TPBVP). The TPBVP is solved under various conditions. The limit case of an infinite time interval is also considered.
Boundary Control Of Pdes
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Author : Miroslav Krstic
language : en
Publisher: SIAM
Release Date : 2008-01-01
Boundary Control Of Pdes written by Miroslav Krstic and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems
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Author : Georges Bastin
language : en
Publisher: Birkhäuser
Release Date : 2016-07-26
Stability And Boundary Stabilization Of 1 D Hyperbolic Systems written by Georges Bastin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-26 with Mathematics categories.
This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.