Boundary Control Of Quasi Linear Hyperbolic Initial Boundary Value Problem

Author : Tatsien Li,Ke Wang,Qilong Gu
Publisher : Springer
Page : 108 pages
File Size : 48,7 Mb
Release : 2016-11-08
Category : Science
ISBN : 9789811028427

Get Book

Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems by Tatsien Li,Ke Wang,Qilong Gu Pdf

This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyperbolic systems.

Author : Jonathan de Halleux
Publisher : Presses univ. de Louvain
Page : 158 pages
File Size : 44,6 Mb
Release : 2004
Category : Science
ISBN : 2930344695

Get Book

Boundary Control of Quasi-Linear Hyperbolic Initial Boundary-Value Problem by Jonathan de Halleux Pdf

The thesis presents different control design approaches for stabilizing networks of quasi-linear hyperbolic partial differential equations. These equations are usually conservative, which gives them interesting properties to design stabilizing control laws. Two main design approaches are developed: a methodology based on entropies and Lyapunov functions and a methodology based on the Riemann invariants. The stability theorems are illustrated using numerical simulations. Two practical applications of these methodologies are presented. Network of navigation channels are modelled using the Saint-Venant equation (also known as the Shallow Water Equations). The stabilization problem of such system has an industrial importance in order to satisfy the navigation constraints and to optimize the production of electricity in hydroelectric plants, usually located at each hydraulic gate. A second application deals with the regulation of water waves in moving tanks. This problem is also modelled by a modified version of the shallow water equations and appears in a number industrial fields which deal with liquid moving parts.

Author : Georges Bastin,Jean-Michel Coron
Publisher : Birkhäuser
Page : 307 pages
File Size : 40,9 Mb
Release : 2016-07-26
Category : Mathematics
ISBN : 9783319320625

Get Book

Stability and Boundary Stabilization of 1-D Hyperbolic Systems by Georges Bastin,Jean-Michel Coron Pdf

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.

Author : Daqian Li
Publisher : Unknown
Page : 340 pages
File Size : 45,7 Mb
Release : 1994-09-06
Category : Mathematics
ISBN : UOM:39015032295712

Get Book

Global Classical Solutions for Quasilinear Hyperbolic Systems by Daqian Li Pdf

A systematic presentation of the global classical solution and the global classical discontinuous solution to quasilinear hyperbolic systems. This book is a result of the author's research on the Cauchy problem, boundary value problems, free boundary problems and the generalised Riemann problem.

Author : Martin Gugat
Publisher : Birkhäuser
Page : 140 pages
File Size : 47,8 Mb
Release : 2015-07-15
Category : Science
ISBN : 9783319188904

Get Book

Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems by Martin Gugat Pdf

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.

Author : Aleksandr Mikhaĭlovich Blokhin,Yuri L. Trakhinin
Publisher : Nova Publishers
Page : 178 pages
File Size : 42,6 Mb
Release : 2006
Category : Mathematics
ISBN : 1594549761

Get Book

Well-posedness of Linear Hyperbolic Problems by Aleksandr Mikhaĭlovich Blokhin,Yuri L. Trakhinin Pdf

"This book will be useful for students and specialists of partial differential equations and the mathematical sciences because it clarifies crucial points of Kreiss' symmetrizer technique. The Kreiss technique was developed by H.O. Kreiss for initial boundary value problems for linear hyperbolic systems. This technique is important because it involves equations that are used in many of the applied sciences. The research presented in this book takes unique approaches to exploring the Kreiss technique that will add insight and new perspectives to linear hyperbolic problems"--Publ. web site.

Author : Yuejun Peng,Bopeng Rao
Publisher : World Scientific
Page : 464 pages
File Size : 54,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814322881

Get Book

Some Problems on Nonlinear Hyperbolic Equations and Applications by Yuejun Peng,Bopeng Rao Pdf

This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.

Author : J. F. Heyda
Publisher : Unknown
Page : 28 pages
File Size : 41,9 Mb
Release : 1959
Category : Boundary value problems
ISBN : UOM:39015086422865

Get Book

Boundary Value Problems for Hyperbolic Partial Differential Equations with Constant Coefficients by J. F. Heyda Pdf

Author : Yiu-Chung Hon,Masahiro Yamamoto,Jin Cheng,June-Yub Lee
Publisher : World Scientific
Page : 472 pages
File Size : 49,7 Mb
Release : 2003-04-08
Category : Technology & Engineering
ISBN : 9789814486026

Get Book

Recent Development in Theories and Numerics by Yiu-Chung Hon,Masahiro Yamamoto,Jin Cheng,June-Yub Lee Pdf

The first International Conference on Inverse Problems was held at the City University of Hong Kong in January 2002. It addressed the theoretical (mathematics), applied (engineering) and development aspects of inverse problems. It was intended to nurture Asian–American–European collaborations in this evolving interdisciplinary area. The scope of the proceedings is wide, reflecting the current flourishing theoretical and numerical researches on inverse problems. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) Contents:SurveysTheoretical AspectsNumerical MethodsSolutions to Applied Inverse ProblemsRelated Topics Readership: Academics, researchers and engineers in applied mathematics. Keywords:Inverse Problems;Applied Mathematics

Author : José F. Rodrigues,Gregory Seregin,José M. Urbano
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 53,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373177

Get Book

Trends in Partial Differential Equations of Mathematical Physics by José F. Rodrigues,Gregory Seregin,José M. Urbano Pdf

This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.

Author : Ströhle, Timo
Publisher : KIT Scientific Publishing
Page : 174 pages
File Size : 40,5 Mb
Release : 2024-02-26
Category : Electronic
ISBN : 9783731513360

Get Book

Inverse dynamics of underactuated flexible mechanical systems governed by quasi-linear hyperbolic partial differential equations by Ströhle, Timo Pdf

This work is about the inverse dynamics of underactuated flexible mechanical systems governed by quasi-linear hyperbolic partial differential equations subjected to time-varying Dirichlet boundary conditions that are enforced by unknown, spatially disjunct, hence non-collocated Neumann boundary conditions.

Author : Valentin Nikolaevich Monakhov,Lev I͡Akovlevich Leĭfman
Publisher : American Mathematical Soc.
Page : 540 pages
File Size : 45,6 Mb
Release : 1983
Category : Mathematics
ISBN : 0821898078

Get Book

Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations by Valentin Nikolaevich Monakhov,Lev I͡Akovlevich Leĭfman Pdf

This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.

Author : Jean-michel Coron,Tatsien Li,Yachun Li
Publisher : World Scientific
Page : 395 pages
File Size : 54,6 Mb
Release : 2019-01-08
Category : Mathematics
ISBN : 9789813276192

Get Book

One-dimensional Hyperbolic Conservation Laws And Their Applications by Jean-michel Coron,Tatsien Li,Yachun Li Pdf

This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

Author : Marco Cirina
Publisher : Unknown
Page : 322 pages
File Size : 48,6 Mb
Release : 1968
Category : Electronic
ISBN : WISC:89011017092

Get Book

On the Boundary Controllability of Nonlinear Hyperbolic Systems by Marco Cirina Pdf

Author : Zhen Hua,Roderick Wong
Publisher : World Scientific
Page : 389 pages
File Size : 53,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9789812560551

Get Book

Differential Equations & Asymptotic Theory in Mathematical Physics by Zhen Hua,Roderick Wong Pdf

This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences