Author: Kong De-XingPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Global Exact Boundary Controllability of a Class of Quasilinear Hyperbolic Systems of Conservation Laws II
Author: Kong De-XingGlobal Exact Boundary Controllability of a Class of Quasilinear Hyperbolic Systems of Conservation Law
Author: De-Xing KongExact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems
Author: Tatsien LiPublisher: Springer
ISBN: 9811028427
Category : Science
Languages : en
Pages : 114
Book Description
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.
One-dimensional Hyperbolic Conservation Laws And Their Applications
Author: Jean-michel CoronPublisher: World Scientific
ISBN: 9813276193
Category : Mathematics
Languages : en
Pages : 395
Book Description
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.
SIAM Journal on Control and Optimization
Author: Society for Industrial and Applied MathematicsPublisher:
ISBN:
Category : Automatic control
Languages : en
Pages : 812
Book Description
Some Problems On Nonlinear Hyperbolic Equations And Applications
Author: Tatsien LiPublisher: World Scientific
ISBN: 981446404X
Category : Mathematics
Languages : en
Pages : 464
Book Description
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.
Boundary Control of Quasi-Linear Hyperbolic Initial Boundary-Value Problem
Author: Jonathan de HalleuxPublisher: Presses univ. de Louvain
ISBN: 9782930344690
Category : Science
Languages : en
Pages : 158
Book Description
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.
Exact Boundary Value Controllability of a Class of Hyperbolic Equations
Author: J. LagneseHyperbolic Systems of Conservation Laws
Author: Alberto BressanPublisher: Oxford University Press, USA
ISBN: 9780198507000
Category : Mathematics
Languages : en
Pages : 270
Book Description
This book provides a self-contained introduction to the mathematical theory of hyperbolic systems of conservation laws, with particular emphasis on the study of discontinuous solutions, characterized by the appearance of shock waves. This area has experienced substantial progress in very recent years thanks to the introduction of new techniques, in particular the front tracking algorithm and the semigroup approach. These techniques provide a solution to the long standing open problems of uniqueness and stability of entropy weak solutions. This volume is the first to present a comprehensive account of these new, fundamental advances. It also includes a detailed analysis of the stability and convergence of the front tracking algorithm. A set of problems, with varying difficulty is given at the end of each chapter to verify and expand understanding of the concepts and techniques previously discussed. For researchers, this book will provide an indispensable reference to the state of the art in the field of hyperbolic systems of conservation laws.
Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems
Author: Martin GugatPublisher:
ISBN: 9783319188911
Category :
Languages : en
Pages :
Book Description
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.