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Author: David Arthur Lawrenz
Publisher:
ISBN:
Category :
Languages : en
Pages : 121
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Book Description
Author: David Arthur Lawrenz
Publisher:
ISBN:
Category :
Languages : en
Pages : 121
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Book Description
Author: Miroslav Krstic
Publisher: SIAM
ISBN: 0898718600
Category : Mathematics
Languages : en
Pages : 197
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Book Description
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.
Author: Martin Gugat
Publisher: Birkhäuser
ISBN: 3319188909
Category : Science
Languages : en
Pages : 143
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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.
Author: Ivan V. Sergienko
Publisher: Springer Science & Business Media
ISBN: 9781402081088
Category : Mathematics
Languages : en
Pages : 410
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Book Description
At present, in order to resolve problems of ecology and to save mineral resources for future population generations, it is quite necessary to know how to maintain nature arrangement in an efficient way. It is possible to achieve a rational nature arrangement when analyzing solutions to problems concerned with optimal control of distributed systems and with optimization of modes in which main ground medium processes are functioning (motion of liquids, generation of temperature fields, mechanical deformation of multicomponent media). Such analysis becomes even more difficult because of heterogeneity of the region that is closest to the Earth surface, and thin inclusions/cracks in it exert their essential influence onto a state and development of the mentioned processes, especially in the cases of mining. Many researchers, for instance, A.N. Tikhonov - A.A. Samarsky [121], L. Luckner - W.M. Shestakow [65], Tien-Mo Shih, K.L. Johnson [47], E. Sanchez-Palencia [94] and others stress that it is necessary to consider how thin inclusions/cracks exert their influences onto development of these processes, while such inclusions differ in characteristics from main media to a considerable extent (moisture permeability, permeability to heat, bulk density or shear strength may be mentioned). Xll An influence exerted from thin interlayers onto examined processes is taken into account sufficiently adequately by means of various constraints, namely, by the conjugation conditions [4, 8, 10, 15, 17-20, 22-26, 38, 44, 47, 52, 53, 68, 76, 77, 81, 83, 84, 90, 95, 96-100, 112-114, 117, 123].
Author: V. Barbu
Publisher: Birkhäuser
ISBN: 303488625X
Category : Science
Languages : en
Pages : 344
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Book Description
This book collects research papers presented in the First Franco Romanian Conference on Optimization, Optimal Control and Partial Differential Equations held at lasi on 7-11 september 1992. The aim and the underlying idea of this conference was to take advantage of the new SOCial developments in East Europe and in particular in Romania to stimulate the scientific contacts and cooperation between French and Romanian mathematicians and teams working in the field of optimization and partial differential equations. This volume covers a large spectrum of problems and result developments in this field in which most of the participants have brought notable contributions. The following topics are discussed in the contributions presented in this volume. 1 -Variational methods in mechanics and physical models Here we mention the contributions of D. Cioranescu. P. Donato and H.I. Ene (fluid flows in dielectric porous media). R. Stavre (the impact of a jet with two fluids on a porous wall). C. Lefter and D. Motreanu (nonlinear eigenvalue problems with discontinuities). I. Rus (maximum principles for elliptic systems). and on asymptotic XII properties of solutions of evolution equations (R Latcu and M. Megan. R Luca and R Morozanu. R Faure). 2 -The controllabillty of Inflnlte dimensional and distributed parameter systems with the contribution of P. Grisvard (singularities and exact controllability for hyperbolic systems). G. Geymonat. P. Loreti and V. Valente (exact controllability of a shallow shell model). C.
Author: Grigory Sklyar
Publisher: Springer Nature
ISBN: 3030617424
Category : Science
Languages : en
Pages : 139
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Book Description
This book presents recent results and envisages new solutions of the stabilization problem for infinite-dimensional control systems. Its content is based on the extended versions of presentations at the Thematic Minisymposium “Stabilization of Distributed Parameter Systems: Design Methods and Applications” at ICIAM 2019, held in Valencia from 15 to 19 July 2019. This volume aims at bringing together contributions on stabilizing control design for different classes of dynamical systems described by partial differential equations, functional-differential equations, delay equations, and dynamical systems in abstract spaces. This includes new results in the theory of nonlinear semigroups, port-Hamiltonian systems, turnpike phenomenon, and further developments of Lyapunov's direct method. The scope of the book also covers applications of these methods to mathematical models in continuum mechanics and chemical engineering. It is addressed to readers interested in control theory, differential equations, and dynamical systems.
Author: F. Kappel
Publisher: Springer
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 476
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Book Description
Author: Charles Teo
Publisher: Academic Press
ISBN: 0080956785
Category : Computers
Languages : en
Pages : 331
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Book Description
Optimal control theory of distributed parameter systems has been a very active field in recent years; however, very few books have been devoted to the studiy of computational algorithms for solving optimal control problems. For this rason the authors decided to write this book. Because the area is so broad, they confined themselves to optimal control problems involving first and second boundary-value problems of a linear second-order parabolic partial differential equation. However the techniques used are by no means restricted to these problems. They can be and in some cases already have been applied to problems involving other types of distributed parameter system. The authors aim is to devise computational algorithms for solving optimal control problems with particular emphasis on the mathematical theory underlying the algorithms. These algorithms are obtained by using a first-order strong variational method or gradient-type methods.
Author: W. Desch
Publisher: Birkhäuser
ISBN: 303488849X
Category : Mathematics
Languages : en
Pages : 308
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Book Description
Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear; - control and identification of nonlinear parabolic systems; - exact and approximate controllability, and observability; - Pontryagin's maximum principle and dynamic programming in PDE; and - numerics pertinent to optimal and suboptimal control problems. This volume is primarily geared toward control theorists seeking information on the latest developments in their area of expertise. It may also serve as a stimulating reader to any researcher who wants to gain an impression of activities at the forefront of a vigorously expanding area in applied mathematics.
Author: Georges Bastin
Publisher: Birkhäuser
ISBN: 3319320629
Category : Mathematics
Languages : en
Pages : 317
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Book Description
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.
