Control Methods In Pde Dynamical Systems

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Control Methods in PDE-Dynamical Systems

Fabio Ancona
Control Methods in PDE Dynamical Systems Book PDF

Author : Fabio Ancona
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 51,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821837665

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Control Methods in PDE-Dynamical Systems by Fabio Ancona Pdf

While rooted in controlled PDE systems, this 2005 AMS-IMS-SIAM Summer Research Conference sought to reach out to a rather distinct, yet scientifically related, research community in mathematics interested in PDE-based dynamical systems. Indeed, this community is also involved in the study of dynamical properties and asymptotic long-time behavior (in particular, stability) of PDE-mixed problems. It was the editors' conviction that the time had become ripe and the circumstances propitious for these two mathematical communities--that of PDE control and optimization theorists and that of dynamical specialists--to come together in order to share recent advances and breakthroughs in their respective disciplines. This conviction was further buttressed by recent discoveries that certain energy methods, initially devised for control-theoretic a-priori estimates, once combined with dynamical systems techniques, yield wholly new asymptotic results on well-established, nonlinear PDE systems, particularly hyperbolic and Petrowski-type PDEs. These expectations are now particularly well reflected in the contributions to this volume, which involve nonlinear parabolic, as well as hyperbolic, equations and their attractors; aero-elasticity, elastic systems; Euler-Korteweg models; thin-film equations; Schrodinger equations; beam equations; etc. In addition, the static topics of Helmholtz and Morrey potentials are also prominently featured. A special component of the present volume focuses on hyperbolic conservation laws, to take advantage of recent theoretical advances with significant implications also on applied problems. In all these areas, the reader will find state-of-the-art accounts as stimulating starting points for further research.

Nonlinear and Robust Control of PDE Systems

Panagiotis D. Christofides
Nonlinear and Robust Control of PDE Systems Book PDF

Author : Panagiotis D. Christofides
Publisher : Springer Science & Business Media
Page : 251 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461201854

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Nonlinear and Robust Control of PDE Systems by Panagiotis D. Christofides Pdf

The interest in control of nonlinear partial differential equation (PDE) sys tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Control of Higher–Dimensional PDEs

Thomas Meurer
Control of Higher Dimensional PDEs Book PDF

Author : Thomas Meurer
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 46,8 Mb
Release : 2012-08-13
Category : Technology & Engineering
ISBN : 9783642300158

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Control of Higher–Dimensional PDEs by Thomas Meurer Pdf

This monograph presents new model-based design methods for trajectory planning, feedback stabilization, state estimation, and tracking control of distributed-parameter systems governed by partial differential equations (PDEs). Flatness and backstepping techniques and their generalization to PDEs with higher-dimensional spatial domain lie at the core of this treatise. This includes the development of systematic late lumping design procedures and the deduction of semi-numerical approaches using suitable approximation methods. Theoretical developments are combined with both simulation examples and experimental results to bridge the gap between mathematical theory and control engineering practice in the rapidly evolving PDE control area. The text is divided into five parts featuring: - a literature survey of paradigms and control design methods for PDE systems - the first principle mathematical modeling of applications arising in heat and mass transfer, interconnected multi-agent systems, and piezo-actuated smart elastic structures - the generalization of flatness-based trajectory planning and feedforward control to parabolic and biharmonic PDE systems defined on general higher-dimensional domains - an extension of the backstepping approach to the feedback control and observer design for parabolic PDEs with parallelepiped domain and spatially and time varying parameters - the development of design techniques to realize exponentially stabilizing tracking control - the evaluation in simulations and experiments Control of Higher-Dimensional PDEs — Flatness and Backstepping Designs is an advanced research monograph for graduate students in applied mathematics, control theory, and related fields. The book may serve as a reference to recent developments for researchers and control engineers interested in the analysis and control of systems governed by PDEs.

Handbook of Dynamical Systems

B. Fiedler
Handbook of Dynamical Systems Book PDF

Author : B. Fiedler
Publisher : Gulf Professional Publishing
Page : 1099 pages
File Size : 55,8 Mb
Release : 2002-02-21
Category : Science
ISBN : 9780080532844

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Handbook of Dynamical Systems by B. Fiedler Pdf

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Control of Nonlinear Dynamical Systems

Felix L. Chernous'ko,I. M. Ananievski,S. A. Reshmin
Control of Nonlinear Dynamical Systems Book PDF

Author : Felix L. Chernous'ko,I. M. Ananievski,S. A. Reshmin
Publisher : Springer Science & Business Media
Page : 398 pages
File Size : 47,6 Mb
Release : 2008-09-26
Category : Technology & Engineering
ISBN : 9783540707844

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Control of Nonlinear Dynamical Systems by Felix L. Chernous'ko,I. M. Ananievski,S. A. Reshmin Pdf

This book is devoted to new methods of control for complex dynamical systems and deals with nonlinear control systems having several degrees of freedom, subjected to unknown disturbances, and containing uncertain parameters. Various constraints are imposed on control inputs and state variables or their combinations. The book contains an introduction to the theory of optimal control and the theory of stability of motion, and also a description of some known methods based on these theories. Major attention is given to new methods of control developed by the authors over the last 15 years. Mechanical and electromechanical systems described by nonlinear Lagrange’s equations are considered. General methods are proposed for an effective construction of the required control, often in an explicit form. The book contains various techniques including the decomposition of nonlinear control systems with many degrees of freedom, piecewise linear feedback control based on Lyapunov’s functions, methods which elaborate and extend the approaches of the conventional control theory, optimal control, differential games, and the theory of stability. The distinctive feature of the methods developed in the book is that the c- trols obtained satisfy the imposed constraints and steer the dynamical system to a prescribed terminal state in ?nite time. Explicit upper estimates for the time of the process are given. In all cases, the control algorithms and the estimates obtained are strictly proven.

Linear, Time-varying Approximations to Nonlinear Dynamical Systems

Maria Tomas-Rodriguez,Stephen P. Banks
Linear Time varying Approximations to Nonlinear Dynamical Systems Book PDF

Author : Maria Tomas-Rodriguez,Stephen P. Banks
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 49,9 Mb
Release : 2010-02-04
Category : Mathematics
ISBN : 9781849961004

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Linear, Time-varying Approximations to Nonlinear Dynamical Systems by Maria Tomas-Rodriguez,Stephen P. Banks Pdf

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Stabilization of Distributed Parameter Systems: Design Methods and Applications

Grigory Sklyar,Alexander Zuyev
Stabilization of Distributed Parameter Systems Design Methods and Applications Book PDF

Author : Grigory Sklyar,Alexander Zuyev
Publisher : Springer Nature
Page : 139 pages
File Size : 51,8 Mb
Release : 2021-03-01
Category : Science
ISBN : 9783030617424

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Stabilization of Distributed Parameter Systems: Design Methods and Applications by Grigory Sklyar,Alexander Zuyev Pdf

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.

Constrained Optimization and Optimal Control for Partial Differential Equations

Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich
Constrained Optimization and Optimal Control for Partial Differential Equations Book PDF

Author : Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 55,9 Mb
Release : 2012-01-03
Category : Mathematics
ISBN : 9783034801331

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Constrained Optimization and Optimal Control for Partial Differential Equations by Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich Pdf

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.

PDE Modeling and Boundary Control for Flexible Mechanical System

Zhijie Liu,Jinkun Liu
PDE Modeling and Boundary Control for Flexible Mechanical System Book PDF

Author : Zhijie Liu,Jinkun Liu
Publisher : Springer Nature
Page : 184 pages
File Size : 55,9 Mb
Release : 2020-03-16
Category : Technology & Engineering
ISBN : 9789811525964

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PDE Modeling and Boundary Control for Flexible Mechanical System by Zhijie Liu,Jinkun Liu Pdf

This book provides a comprehensive review of fundamental issues in the dynamical modeling and vibration control design for several flexible mechanical systems, such as flexible satellites, flexible aerial refueling hoses, and flexible three-dimensional manipulators. Offering an authoritative reference guide to the dynamics and control of flexible mechanical systems, it equips readers to solve a host of problems concerning these systems. It provides not only a complete overview of flexible systems, but also a better understanding of the technical levels involved. The book is divided into ten chapters: Chapters 1 and 2 lay the foundations, while the remaining chapters explore several independent yet related topics in detail. The book’s final chapter presents conclusions and recommendations for future research. Given its scope, the book is intended for researchers, graduate students, and engineers whose work involves control systems, flexible mechanical systems, and related areas.

Boundary Control of PDEs

Miroslav Krstic,Andrey Smyshlyaev
Boundary Control of PDEs Book PDF

Author : Miroslav Krstic,Andrey Smyshlyaev
Publisher : SIAM
Page : 197 pages
File Size : 49,7 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718607

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Boundary Control of PDEs by Miroslav Krstic,Andrey Smyshlyaev Pdf

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.

Recent Advances in Control Problems of Dynamical Systems and Networks

Ju H. Park
Recent Advances in Control Problems of Dynamical Systems and Networks Book PDF

Author : Ju H. Park
Publisher : Springer Nature
Page : 548 pages
File Size : 43,8 Mb
Release : 2020-08-11
Category : Technology & Engineering
ISBN : 9783030491239

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Recent Advances in Control Problems of Dynamical Systems and Networks by Ju H. Park Pdf

This edited book introduces readers to new analytical techniques and controller design schemes used to solve the emerging “hottest” problems in dynamic control systems and networks. In recent years, the study of dynamic systems and networks has faced major changes and challenges with the rapid advancement of IT technology, accompanied by the 4th Industrial Revolution. Many new factors that now have to be considered, and which haven’t been addressed from control engineering perspectives to date, are naturally emerging as the systems become more complex and networked. The general scope of this book includes the modeling of the system itself and uncertainty elements, examining stability under various criteria, and controller design techniques to achieve specific control objectives in various dynamic systems and networks. In terms of traditional stability matters, this includes the following special issues: finite-time stability and stabilization, consensus/synchronization, fault-tolerant control, event-triggered control, and sampled-data control for classical linear/nonlinear systems, interconnected systems, fractional-order systems, switched systems, neural networks, and complex networks. In terms of introducing graduate students and professional researchers studying control engineering and applied mathematics to the latest research trends in the areas mentioned above, this book offers an excellent guide.

Stabilization, Optimal and Robust Control

Aziz Belmiloudi
Stabilization Optimal and Robust Control Book PDF

Author : Aziz Belmiloudi
Publisher : Springer Science & Business Media
Page : 509 pages
File Size : 49,7 Mb
Release : 2008-08-17
Category : Technology & Engineering
ISBN : 9781848003446

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Stabilization, Optimal and Robust Control by Aziz Belmiloudi Pdf

Stabilization, Optimal and Robust Control develops robust control of infinite-dimensional dynamical systems derived from time-dependent coupled PDEs associated with boundary-value problems. Rigorous analysis takes into account nonlinear system dynamics, evolutionary and coupled PDE behaviour and the selection of function spaces in terms of solvability and model quality. Mathematical foundations are provided so that the book remains accessible to the non-control-specialist. Following chapters giving a general view of convex analysis and optimization and robust and optimal control, problems arising in fluid mechanical, biological and materials scientific systems are laid out in detail. The combination of mathematical fundamentals with application of current interest will make this book of much interest to researchers and graduate students looking at complex problems in mathematics, physics and biology as well as to control theorists.

Control of Partial Differential Equations

Giuseppe Da Prato,Luciano Tubaro
Control of Partial Differential Equations Book PDF

Author : Giuseppe Da Prato,Luciano Tubaro
Publisher : CRC Press
Page : 302 pages
File Size : 48,5 Mb
Release : 1994-08-19
Category : Mathematics
ISBN : 0824792408

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Control of Partial Differential Equations by Giuseppe Da Prato,Luciano Tubaro Pdf

This useful reference provides recent results as well as entirely new material on control problems for partial differential equations.

Industrial Mathematics and Complex Systems

Pammy Manchanda,René Lozi,Abul Hasan Siddiqi
Industrial Mathematics and Complex Systems Book PDF

Author : Pammy Manchanda,René Lozi,Abul Hasan Siddiqi
Publisher : Springer
Page : 357 pages
File Size : 44,9 Mb
Release : 2017-10-18
Category : Mathematics
ISBN : 9789811037580

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Industrial Mathematics and Complex Systems by Pammy Manchanda,René Lozi,Abul Hasan Siddiqi Pdf

The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business transactions, and brain-like computers are also highlighted. These contributions – all prepared by respected academicians, scientists and researchers from across the globe – are based on papers presented at the international conference organized on the occasion of the Silver Jubilee of the Indian Society of Industrial and Applied Mathematics (ISIAM) held from 29 to 31 January 2016 at Sharda University, Greater Noida, India. The book will help young scientists and engineers grasp systematic developments in those areas of mathematics that are essential to properly understand challenging contemporary problems.

Optimal Control of Partial Differential Equations

Andrea Manzoni,Alfio Quarteroni,Sandro Salsa
Optimal Control of Partial Differential Equations Book PDF

Author : Andrea Manzoni,Alfio Quarteroni,Sandro Salsa
Publisher : Springer Nature
Page : 507 pages
File Size : 41,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030772260

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Optimal Control of Partial Differential Equations by Andrea Manzoni,Alfio Quarteroni,Sandro Salsa Pdf

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.