Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon

Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon PDF

Author: Irena Lasiecka

Publisher: Cambridge University Press

Published: 2011-04-14

Total Pages: 0

ISBN-13: 9780521155687

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Volume II focuses on the optimal control problem over a finite time interval for hyperbolic dynamical systems. The chapters consider some abstract models, each motivated by a particular canonical hyperbolic dynamics, and present numerous new results.

Robust Engineering Designs of Partial Differential Systems and Their Applications

Robust Engineering Designs of Partial Differential Systems and Their Applications PDF

Author: Bor-Sen Chen

Publisher: CRC Press

Published: 2021-12-22

Total Pages: 459

ISBN-13: 1000514064

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Considers both time‐domain and frequency domain robust design techniques of partial differential systems Illustrates both theoretical robust design techniques and practical applications Discusses partial differential systems with both Dirichlet and Neuman boundary conditions in robust design procedure Addresses deterministic and stochastic partial differential systems Explores theoretical mathematical background, robust signal processing design, robust control system design and robust biological system design with application

Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws

Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws PDF

Author: Krzysztof Bartecki

Publisher: Springer

Published: 2015-12-21

Total Pages: 146

ISBN-13: 3319275011

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This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange center as well as from his research experience in the field of mathematical and computer modeling of dynamic systems. The book presents valuable results concerning their state-space, transfer function and time-domain representations, which can be useful both for the open-loop analysis as well as for the closed-loop design. The book is primarily intended to help professionals as well as undergraduate and postgraduate students involved in modeling and automatic control of dynamic systems.

Infinite Dimensional Linear Control Systems

Infinite Dimensional Linear Control Systems PDF

Author:

Publisher: Elsevier

Published: 2005-07-12

Total Pages: 332

ISBN-13: 0080457347

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For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike

Controllability of Dynamic Systems

Controllability of Dynamic Systems PDF

Author: Ara S. Avetisyan

Publisher: Cambridge Scholars Publishing

Published: 2018-04-03

Total Pages: 223

ISBN-13: 1527509133

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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.

Numerical Control: Part A

Numerical Control: Part A PDF

Author:

Publisher: Elsevier

Published: 2022-02-15

Total Pages: 596

ISBN-13: 0323853390

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Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control

Turnpike Conditions in Infinite Dimensional Optimal Control

Turnpike Conditions in Infinite Dimensional Optimal Control PDF

Author: Alexander J. Zaslavski

Publisher: Springer

Published: 2019-07-23

Total Pages: 570

ISBN-13: 3030201783

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This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results.

Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems

Optimal Boundary Control and Boundary Stabilization of Hyperbolic Systems PDF

Author: Martin Gugat

Publisher: Birkhäuser

Published: 2015-07-15

Total Pages: 140

ISBN-13: 3319188909

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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.

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