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Optimal Control Of Nonlinear Parabolic Systems
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Book Synopsis Optimal Control of Nonlinear Parabolic Systems by : Pekka Neittaanmaki
Download or read book Optimal Control of Nonlinear Parabolic Systems written by Pekka Neittaanmaki and published by CRC Press. This book was released on 1994-02-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses theoretical approaches to the study of optimal control problems governed by non-linear evolutions - including semi-linear equations, variational inequalities and systems with phase transitions. It also provides algorithms for solving non-linear parabolic systems and multiphase Stefan-like systems.
Book Synopsis MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs by :
Download or read book MPC/LQG-Based Optimal Control of Nonlinear Parabolic PDEs written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this thesis is the theoretical and numerical research of optimal control problems for uncertain nonlinear systems, described by semilinear parabolic differential equations with additive noise, where the state is not completely available. Based on a paper by Kazufumi Ito and Karl Kunisch, which was published in 2006 with the title "Receding Horizon Control with Incomplete Observations", we analyze a Model Predictive Control (MPC) approach where the resulting linear problems on small intervals are solved with a Linear Quadratic Gaussian (LQG) design. Further we define a performance index for the MPC/LQG approach, find estimates for it and present bounds for the solutions of the underlying Riccati equations. Another large part of the thesis is devoted to extensive numerical studies for an 1+1- and 3+1-dimensional problem to show the robustness of the MPC/LQG strategy. The last part is a generalization of the MPC/LQG approach to infinite-dimensional problems.
Book Synopsis Optimal Control for Nonlinear Parabolic Distributed Parameter Systems by : Quan-Fang Wang
Download or read book Optimal Control for Nonlinear Parabolic Distributed Parameter Systems written by Quan-Fang Wang and published by LAP Lambert Academic Publishing. This book was released on 2011 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, we have studied the quadratic cost optimal control problems and their numerical analysis of nonlinear parabolic distributed parameter systems. After established the fundamental existence and uniqueness results, we have developed the nonlinear optimal control theory for the equations having uniform Lipschitz continuous nonlinearity. Then we have applied the theoretical results to practical nonlinear parabolic partial differential equations including reaction-diffusion equations, diffusion Hopfield neural network equations. Furthermore, numerical evidences for these issues have also been solved by using variational method and finite element approach.
Book Synopsis MPC/LQG Based Optimal Control of Nonlinear Parabolic PDEs by : Sabine Hein
Download or read book MPC/LQG Based Optimal Control of Nonlinear Parabolic PDEs written by Sabine Hein and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Control and Estimation of Distributed Parameter Systems by : W. Desch
Download or read book Control and Estimation of Distributed Parameter Systems written by W. Desch and published by Springer Science & Business Media. This book was released on 1998-03-24 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear and Optimal Control Systems by : Thomas L. Vincent
Download or read book Nonlinear and Optimal Control Systems written by Thomas L. Vincent and published by John Wiley & Sons. This book was released on 1997-06-23 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback control systems. There is special emphasis on the fundamental topics of stability, controllability, and optimality, and on the corresponding geometry associated with these topics. Each chapter contains several examples and a variety of exercises.
Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch
Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Society. This book was released on 2024-03-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.
Book Synopsis Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems by : Songmu Zheng
Download or read book Nonlinear Parabolic Equations and Hyperbolic-Parabolic Coupled Systems written by Songmu Zheng and published by CRC Press. This book was released on 1995-08-08 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the global existence, uniqueness and asymptotic behaviour of smooth solutions to both initial value problems and initial boundary value problems for nonlinear parabolic equations and hyperbolic parabolic coupled systems. Most of the material is based on recent research carried out by the author and his collaborators. The book can be divided into two parts. In the first part, the results on decay of solutions to nonlinear parabolic equations and hyperbolic parabolic coupled systems are obtained, and a chapter is devoted to the global existence of small smooth solutions to fully nonlinear parabolic equations and quasilinear hyperbolic parabolic coupled systems. Applications of the results to nonlinear thermoelasticity and fluid dynamics are also shown. Some nonlinear parabolic equations and coupled systems arising from the study of phase transitions are investigated in the second part of the book. The global existence, uniqueness and asymptotic behaviour of smooth solutions with arbitrary initial data are obtained. The final chapter is further devoted to related topics: multiplicity of equilibria and the existence of a global attractor, inertial manifold and inertial set. A knowledge of partial differential equations and Sobolev spaces is assumed. As an aid to the reader, the related concepts and results are collected and the relevant references given in the first chapter. The work will be of interest to researchers and graduate students in pure and applied mathematics, mathematical physics and applied sciences.
Book Synopsis Numerical Study for Optimal Control Problems of Parabolic Systems by : Talaat Abdelhamid
Download or read book Numerical Study for Optimal Control Problems of Parabolic Systems written by Talaat Abdelhamid and published by LAP Lambert Academic Publishing. This book was released on 2015-02-18 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: The optimal control problems governed by partial differential equations have developed very fast in the last 30 years, and it has brought a promising and vital researching domain to the subject of mathematics. The optimal control problems governed by partial differential equations concern many applications in physics, chemistry, biology, etc., such as materials design, crystal growth, temperature control, petroleum exploitation, and so on. The partial differential equations involved in these problems include elliptic equations, parabolic equations and hyperbolic equations. Our objective of this book, which consists of three chapters, aims to introduce the analytical and numerical solutions of constrained optimal control problems of quasilinear parabolic systems.
Book Synopsis Control Of Nonlinear Distributed Parameter Systems by : Goong Chen
Download or read book Control Of Nonlinear Distributed Parameter Systems written by Goong Chen and published by CRC Press. This book was released on 2001-03-14 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics a
Book Synopsis Optimal Control of Parabolic Systems with Multiple Time Lags by : Adam Kowalewski
Download or read book Optimal Control of Parabolic Systems with Multiple Time Lags written by Adam Kowalewski and published by . This book was released on 1997 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis PRACTICAL APPLICATION O OPTIMAL CONTROL THEORY by : QUAN-FANG WANG
Download or read book PRACTICAL APPLICATION O OPTIMAL CONTROL THEORY written by QUAN-FANG WANG and published by Lambert Academic Publishing. This book was released on 2011-11-11 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Karl-Heinz Hoffmann Publisher :Springer Science & Business Media ISBN 13 :9783764361518 Total Pages :344 pages Book Rating :4.3/5 (615 download)
Book Synopsis Optimal Control of Partial Differential Equations by : Karl-Heinz Hoffmann
Download or read book Optimal Control of Partial Differential Equations written by Karl-Heinz Hoffmann and published by Springer Science & Business Media. This book was released on 1999 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-posedness of Semilinear Heat Equations with Iterated Logarithms.- Uniform Stability of Nonlinear Thermoelastic Plates with Free Boundary Conditions.- Exponential Bases in Sobolev Spaces in Control and Observation Problems.- Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems.- Discretization of the Controllability Grammian in View of Exact Boundary Control: the Case of Thin Plates.- Stability of Holomorphic Semigroup Systems under Nonlinear Boundary Perturbations.- Shape Control in Hyperbolic Problems.- Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints.- Intrinsic P(2, 1) Thin Shell Models and Naghdi's Models without A Priori Assumption on the Stress Tensor.- On the Approximate Controllability for some Explosive Parabolic Problems.- Fréchet-Differentiability and Sufficient Optimality Conditions for Shape Functionals.- State Constrained Optimal Control for some Quasilinear Parabolic Equations.- Controllability property for the Navier-Stokes equations.- Shape Sensitivity and Large Deformation of the Domain for Norton-Hoff Flows.- On a Distributed Control Law with an Application to the Control of Unsteady Flow around a Cylinder.- Homogenization of a Model Describing Vibration of Nonlinear Thin Plates Excited by Piezopatches.- Stabilization of the Dynamic System of Elasticity by Nonlinear Boundary Feedback.- Griffith Formula and Rice-Cherepanov's Integral for Elliptic Equations with Unilateral Conditions in Nonsmooth Domains.- A Domain Optimization Problem for a Nonlinear Thermoelastic System.- Approximate Controllability for a Hydro-Elastic Model in a Rectangular Domain.- Noncooperative Games with Elliptic Systems.- Incomplete Indefinite Decompositions as Multigrid Smoothers for KKT Systems.- Domain Optimization for the Navier-Stokes Equations by an Embedding Domain Method.- On the Approximation and Optimization of Fourth Order Elliptic Systems.- On the Existence and Approximation of Solutions for the Optimal Control of Nonlinear Hyperbolic Conservation Laws.- Identification of Memory Kernels in Heat Conduction and Viscoelasticity.- Variational Formulation for Incompressible Euler Equation by Weak Shape Evolution.
Book Synopsis Optimal Control of a Class of Nonlinear Parabolic PDE Systems Arising in Fusion Plasma Current Profile Dynamics by : Yongsheng Ou
Download or read book Optimal Control of a Class of Nonlinear Parabolic PDE Systems Arising in Fusion Plasma Current Profile Dynamics written by Yongsheng Ou and published by . This book was released on 2010 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion arises as a potential source of energy with sufficient energy density to supply the world population with its steadily increasing energy demands.
Book Synopsis Nonlinear Controllability and Optimal Control by : Sussmann
Download or read book Nonlinear Controllability and Optimal Control written by Sussmann and published by Routledge. This book was released on 2017-11-22 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections ... Lie algebraic conditions for local controllability... the use of the Campbell-Hausdorff series to derive properties of optimal trajectories... the Fuller phenomenon ... the theory of orbits ... and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .
Book Synopsis Control and Estimation of Distributed Parameter Systems by : W. Desch
Download or read book Control and Estimation of Distributed Parameter Systems written by W. Desch and published by Birkhäuser. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Optimal Control Theory by : Leonard David Berkovitz
Download or read book Nonlinear Optimal Control Theory written by Leonard David Berkovitz and published by CRC Press. This book was released on 2012-08-25 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also discusses Hamilton-Jacobi theory. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, partial differential equations, and differential games.
