Download or read book Quadratic Functionals in Variational Analysis and Control Theory written by Werner Kratz and published by Wiley-VCH. This book was released on 1995-04-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended to provide classical and recent results on quadratic functionals. On the one hand it contains the well-known facts on the second variation from the calculus of variations, including Jacobi-type conditions, and on the other hand new aspects in control theory, in particular the notion of strong observability and its relation to the optimal linear regulator. The main object described is a general theory of self-adjoint eigenvalue problems for linear Hamiltonian systems, which includes Morse's oscillation theory and his extensions of Sturmian theory. The dependence on the eigenvalue parameter may be nonlinear. The treatment is based on a novel approach via field theory, in particular Picone's identity. The central features needed for the method are recent results on Riccati matrix differential equations and on monotone matrix-valued functions. Applications of the theory yield classical and new results in such areas as, for example, linear control theory, variational analysis (Rayleigh's principle), or Sturm-Liouville eigenvalue problems. The book is self-contained, and accessible to mathematics or science students entering the graduate level.
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Download or read book Variational Calculus Optimal Control and Applications written by Rolf Klötzler and published by Springer Science & Business Media. This book was released on 1998 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the Convexification of Optimal Control Problems of Flight Dynamics.- Restricted Optimal Transportation Flows.- Relaxation Gaps in Optimal Control Processes with State Constraints.- Optimal Shape Design for Elliptic Hemivariational Inequalities in Nonlinear Elasticity.- A Discretization for Control Problems with optimality test.- Smooth and Nonsmooth Optimal Lipschitz Control - a Model Problem.- Suboptimality Theorems in Optimal Control.- A Second Order Sufficient Condition for Optimality in Nonlinear Control - the Conjugate Point Approach.- Extremal Problems for Elliptic Systems.- Existence Results for Some Nonconvex Optimization Problems Governed by Nonlinear Processes.- Multiobjective Optimal Control Problems.- Existence Principles and the Theory of Extremal Problems.- Hamilton-Jacobi-Bellman Equations and Optimal Control.- Output Target Control and Uncertain Infinite-Dimensional Systems.- Sensitivity Analysis of Stiff and Non-stiff Initial-value Problems.- Algorithm of Real-Time Minimization of Control Norm for Incompletely Determined Linear Control Systems.- Set-valued Calculus and Dynamic Programming in Problems of Feedback Control.- Strong Observability of Time-dependent Linear Systems.- Sensitivity Analysis and Real-Time Control of Nonlinear Optimal Control Systems via Nonlinear Programming Methods.- Accelerating Multiple Shooting for State-constrained Trajectory Optimization Problems.- SQP Methods and their Application to Numerical Optimal Control.- Predictor-Corrector Continuation Method for Optimal Control Problems.- Time Invariant Global Stabilization of a Mobile Robot.- Competitive Running on a Hilly Track.- Convex Domains of Given Diameter with Greatest Volume.- Isoperimetric and Isodiametric Area-minimal Plane Convex Figures.- Minimizing the Noise of an Aircraft during Landing Approach.- Real-Time Computation of Strategies of Differential Games with Applications to Collision Avoidance.- The Use of Screening for the Control of an Endemic Disease.- Optimal Control of Sloshing Liquids.- Free Surface Waves in a Wave Tank.- Efficient Convexification of Flight Path Optimization Problems.- Determining the Controllability Region for the Re-entry of an Apollo-type Spacecraft.
Download or read book Discrete Dynamics And Difference Equations Proceedings Of The Twelfth International Conference On Difference Equations And Applications written by Saber N Elaydi and published by World Scientific. This book was released on 2010-11-02 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume holds a collection of articles based on the talks presented at ICDEA 2007 in Lisbon, Portugal.The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.
Download or read book Variational Analysis written by Marston Morse and published by Courier Corporation. This book was released on 2013-02-27 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents extended separation, comparison, and oscillation theorems that replace classical analysis. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals. 1973 edition.
Download or read book Discrete Oscillation Theory written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2005 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory. In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks. The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.
Download or read book Stochastic and Infinite Dimensional Analysis written by Christopher C. Bernido and published by Birkhäuser. This book was released on 2016-08-10 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Download or read book Nonautonomous Linear Hamiltonian Systems Oscillation Spectral Theory and Control written by Russell Johnson and published by Springer. This book was released on 2016-03-25 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hamiltonian systems of general dimension. The properties of all these objects form the basis for the study of several themes concerning linear-quadratic control problems, including the linear regulator property, the Kalman-Bucy filter, the infinite-horizon optimization problem, the nonautonomous version of the Yakubovich Frequency Theorem, and dissipativity in the Willems sense. The book will be useful for graduate students and researchers interested in nonautonomous differential equations; dynamical systems and ergodic theory; spectral theory of differential operators; and control theory.
Download or read book Difference Equations Special Functions and Orthogonal Polynomials written by Saber Elaydi and published by World Scientific. This book was released on 2007 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Download or read book Lyapunov Inequalities and Applications written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2021-04-12 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.
Download or read book Difference Equations Special Functions And Orthogonal Polynomials Proceedings Of The International Conference written by Jim M Cushing and published by World Scientific. This book was released on 2007-05-21 with total page 789 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains talks given at a joint meeting of three communities working in the fields of difference equations, special functions and applications (ISDE, OPSFA, and SIDE). The articles reflect the diversity of the topics in the meeting but have difference equations as common thread. Articles cover topics in difference equations, discrete dynamical systems, special functions, orthogonal polynomials, symmetries, and integrable difference equations.
Download or read book Sturm Liouville Theory written by Werner O. Amrein and published by Springer Science & Business Media. This book was released on 2005-05-19 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of survey articles based on lectures presented at a colloquium and workshop in Geneva in 2003 to commemorate the 200th anniversary of the birth of Charles François Sturm. It aims at giving an overview of the development of Sturm-Liouville theory from its historical roots to present day research. It is the first time that such a comprehensive survey has been made available in compact form. The contributions come from internationally renowned experts and cover a wide range of developments of the theory. The book can therefore serve both as an introduction to Sturm-Liouville theory and as background for ongoing research. The volume is addressed to researchers in related areas, to advanced students and to those interested in the historical development of mathematics. The book will also be of interest to those involved in applications of the theory to diverse areas such as engineering, fluid dynamics and computational spectral analysis.
Download or read book Matrix Riccati Equations in Control and Systems Theory written by Hisham Abou-Kandil and published by Birkhäuser. This book was released on 2012-12-06 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
Download or read book Symplectic Difference Systems Oscillation and Spectral Theory written by Ondřej Došlý and published by Springer Nature. This book was released on 2019-09-06 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.
Download or read book Advances in Difference Equations written by Saber N. Elaydi and published by CRC Press. This book was released on 1998-01-29 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent surge in research activity in difference equations and applications has been driven by the wide applicability of discrete models to such diverse fields as biology, engineering, physics, economics, chemistry, and psychology. The 68 papers that make up this book were presented by an international group of experts at the Second International Conference on Difference Equations, held in Veszprém, Hungary, in August, 1995. Featuring contributions on such topics as orthogonal polynomials, control theory, asymptotic behavior of solutions, stability theory, special functions, numerical analysis, oscillation theory, models of vibrating string, models of chemical reactions, discrete competition systems, the Liouville-Green (WKB) method, and chaotic phenomena, this volume offers a comprehensive review of the state of the art in this exciting field.
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
