Download or read book Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems written by Martin Gugat and published by Birkhäuser. This book was released on 2015-07-15 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Singularities in Boundary Value Problems written by Pierre Grisvard and published by Springer. This book was released on 1992 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Control of PDEs written by Miroslav Krstic and published by SIAM. This book was released on 2008-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optimization Optimal Control and Partial Differential Equations written by Viorel Barbu and published by Springer Science & Business Media. This book was released on 1992 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational methods in mechanics and physical models.- Fluid flows in dielectric porous media.- The impact of a jet with two fluids on a porous wall.- Critical point methods in nonlinear eigenvalue problems with discontinuities.- Maximum principles for elliptic systems.- Exponential dichotomy of evolution operators in Banach spaces.- Asymptotic properties of solutions to evolution equations.- On some nonlinear elastic waves biperiodical or almost periodical in mechanics and extensions hyperbolic nonlinear partial differential equations.- The controllability of infinite dimensional and distributed parameter systems.- Singularities in boundary value problems and exact controllability of hyperbolic systems.- Exact controllability of a shallow shell model.- Inverse problem: Identification of a melting front in the 2D case.- Micro-local approach to the control for the plates equation.- Bounded solutions for controlled hyperbolic systems.- Controllability and turbulence.- The H? control problem.- The H? boundary control with state feedback; the hyperbolic case.- Remarks on the theory of robust control.- The dynamic programming method.- Optimality and characteristics of Hamilton-Jacobi-Bellman equations.- Verification theorems of dynamic programming type in optimal control.- Isaacs' equations for value-functions of differential games.- Optimal control for robot manipulators.- Control theory and environmental problems: Slow fast models for management of renewable ressources.- On the Riccati equations of stochastic control.- Optimal control of nonlinear partial differential equations.- A boundary Pontryagin's principle for the optimal control of state-constrained elliptic systems.- Controllability properties for elliptic systems, the fictitious domain method and optimal shape design problems.- Optimal control for elliptic equation and applications.- Inverse problems for variational inequalities.- The variation of the drag with respect to the domain in Navier-Stokes flow, .- Mathematical programming and nonsmooth optimization.- Scalar minimax properties in vectorial optimization.- Least-norm regularization for weak two-level optimization problems.- Continuity of the value function with respect to the set of constraints.- On integral inequalities involving logconcave functions.- Numerical solution of free boundary problems in solids mechanics.- Authors' index
Download or read book Exact Controllability and Stabilization of the Wave Equation written by Enrique Zuazua and published by Springer Nature. This book was released on with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Synchronization for Hyperbolic Systems written by Tatsien Li and published by Springer Nature. This book was released on 2019-12-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Exact Controllability and Stabilization written by V. Komornik and published by Elsevier Masson. This book was released on 1994 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stability and Boundary Stabilization of 1 D Hyperbolic Systems written by Georges Bastin and published by Birkhäuser. This book was released on 2016-07-26 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Wave Equations written by Tatsien Li and published by Springer. This book was released on 2017-11-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Download or read book Control and Nonlinearity written by Jean-Michel Coron and published by American Mathematical Soc.. This book was released on 2007 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods to study the controllability and the stabilization of nonlinear control systems in finite and infinite dimensions. The emphasis is put on specific phenomena due to nonlinearities. In particular, many examples are given where nonlinearities turn out to be essential to get controllability or stabilization. Various methods are presented to study the controllability or to construct stabilizing feedback laws. The power of these methods is illustrated by numerous examples coming from such areas as celestial mechanics, fluid mechanics, and quantum mechanics. The book is addressed to graduate students in mathematics or control theory, and to mathematicians or engineers with an interest in nonlinear control systems governed by ordinary or partial differential equations.
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 2003 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperbolic Systems of Conservation Laws written by Alberto Bressan and published by Oxford University Press, USA. This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 2003 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Controllability of Dynamic Systems written by Ara S. Avetisyan and published by Cambridge Scholars Publishing. This book was released on 2018-04-03 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about the possibilities of involvement of the well-known Green’s function method in exact or approximate controllability analysis for dynamic systems. Due to existing extensions of the Green’s function notion to nonlinear systems, the approach developed here is valid for systems with both linear and nonlinear dynamics. The book offers a number of particular examples, covering specific issues that make the controllability analysis sophisticated, such as coordinate dependent characteristics, point sources, unbounded domains, higher dimensions, and specific nonlinearities. It also offers extensive numerical analysis, which reveals both advantages and drawbacks of the approach. As such, the book will be of interest to researchers interested in the theory and practice of control, as well as PhD and Master’s students.
Download or read book Adaptive Control of Hyperbolic PDEs written by Henrik Anfinsen and published by Springer. This book was released on 2019-02-21 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive Control of Linear Hyperbolic PDEs provides a comprehensive treatment of adaptive control of linear hyperbolic systems, using the backstepping method. It develops adaptive control strategies for different combinations of measurements and actuators, as well as for a range of different combinations of parameter uncertainty. The book treats boundary control of systems of hyperbolic partial differential equations (PDEs) with uncertain parameters. The authors develop designs for single equations, as well as any number of coupled equations. The designs are accompanied by mathematical proofs, which allow the reader to gain insight into the technical challenges associated with adaptive control of hyperbolic PDEs, and to get an overview of problems that are still open for further research. Although stabilization of unstable systems by boundary control and boundary sensing are the particular focus, state-feedback designs are also presented. The book also includes simulation examples with implementational details and graphical displays, to give readers an insight into the performance of the proposed control algorithms, as well as the computational details involved. A library of MATLAB® code supplies ready-to-use implementations of the control and estimation algorithms developed in the book, allowing readers to tailor controllers for cases of their particular interest with little effort. These implementations can be used for many different applications, including pipe flows, traffic flow, electrical power lines, and more. Adaptive Control of Linear Hyperbolic PDEs is of value to researchers and practitioners in applied mathematics, engineering and physics; it contains a rich set of adaptive control designs, including mathematical proofs and simulation demonstrations. The book is also of interest to students looking to expand their knowledge of hyperbolic PDEs.
Download or read book Representation and Control of Infinite Dimensional Systems written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.
Download or read book Fourier Series in Control Theory written by Vilmos Komornik and published by Springer Science & Business Media. This book was released on 2005-11-03 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first serious attempt to gather all of the available theory of "nonharmonic Fourier series" in one place, combining published results with new results by the authors.
