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Mathematical control theory of applied partial differential equations is built on linear andnonlinearfunctionalanalysisand manyexistencetheoremsin controlt- ory result from applications of theorems in functional analysis. This makes control theoryinaccessibleto studentswhodo nothave a backgroundin functionalanalysis. Many advanced control theory books on in?nite-dimensionalsystems were wr- ten, using functional analysis and semigroup theory, and control theory was p- sented in an abstract setting. This motivates me to write this text for control theory classes in the way to present control theory by concrete examples and try to m- imize the use of functional analysis. Functional analysis is not assumed and any analysis included here is elementary, using calculus such as integration by parts. The material presented in this text is just a simpli?cation of the material from the existing advanced control books. Thus this text is accessible to senior undergra- ate studentsand?rst-yeargraduatestudentsin appliedmathematics,who havetaken linear algebra and ordinary and partial differential equations. Elementary functional analysis is presented in Chapter 2. This material is - quired to present the control theory of partial differential equations. Since many control conceptsand theories for partial differentialequations are transplanted from ?nite-dimensionalcontrol systems, a brief introduction to feedback control of these systemsispresentedinChapter3.Thetopicscoveredinthischapterincludecontr- lability, observability,stabilizability, pole placement, and quadratic optimal control.

Mathematics. --- Partial Differential Equations. --- Applications of Mathematics. --- Control. --- Differential equations, partial. --- Mathématiques --- Control theory --- Wave equation --- Control theory. --- Feedback control systems. --- Wave equation.

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This well structured, intriguing and motivating book presents the basic ideas and understanding of control, signals and systems for readers interested in engineering and science. Through a series of examples that are regularly revisited from different perspectives, the book explores both the theory and the practice of control."Feedback and Control for Everyone" is indeed intended for everyone, but more specifically everyone interested in getting a feel for the role control and feedback play in our environment. Control and feedback are pervasive and are literally found everywhere in our engineered or biological environment. The book focuses on the main ideas and opens the scientific mind to feedback, control and systems dynamics. The exposition of ideas does not assume any mathematical knowledge beyond what typically is taught at an intermediate mathematics level at high school. Appealing to examples and intuition, the authors guide the reader to the essential ingredients to describe, analyze and synthesize successfully feedback. Each chapter ends with comments and references that enable the interested reader to explore the exposed subject material in a deeper manner. "Feedback and Control for Everyone" is written for: * understanding basic concepts on systems dynamics and control * realizing the strong connection between technical and human/social dynamics * motivating further reading and study about control systems * showing the power of abstraction to infer properties of complex systems based on simplified mathematical models * emphasizing the interplay between communication, computers and control in this Digital Era * creating bridges among different sciences and technologies such as engineering, physics, biology, biochemistry, or systems dynamics. Credits: the Cover Illustration and Heading chapters were designed by Arturo Mora (www.cut-out.es)

Science --- Mathematics --- Classical mechanics. Field theory --- Mechanical properties of solids --- Electrical engineering --- Applied physical engineering --- Engineering sciences. Technology --- Linguistics --- patroonherkenning --- popularisering wetenschap --- populaire cultuur --- automatisering --- systeemtheorie --- systeembeheer --- ingenieurswetenschappen --- elektrotechniek --- dynamica --- automatische regeltechniek --- optica --- Control theory. --- Feedback control systems. --- Control theory

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This Festschrift, published on the occasion of the sixtieth birthday of Yutaka - mamoto ( ˜YY' as he is occasionally casually referred to), contains a collection of articles by friends, colleagues, and former Ph.D. students of YY. They are a tribute to his friendship and his scienti?c vision and oeuvre, which has been a source of inspiration to the authors. Yutaka Yamamoto was born in Kyoto, Japan, on March 29, 1950. He studied applied mathematics and general engineering science at the Department of Applied Mathematics and Physics of Kyoto University, obtaining the B.S. and M.Sc. degrees in 1972 and 1974. His M.Sc. work was done under the supervision of Professor Yoshikazu Sawaragi. In 1974, he went to the Center for Mathematical System T- ory of the University of Florida in Gainesville. He obtained the M.Sc. and Ph.D. degrees, both in Mathematics, in 1976 and 1978, under the direction of Professor Rudolf Kalman.

Engineering. --- Control , Robotics, Mechatronics. --- Systems Theory, Control. --- Signal, Image and Speech Processing. --- Systems theory. --- Control engineering systems. --- Ingénierie --- System theory --- Control theory --- Signal processing

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This volume—dedicated to Michael K. Sain on the occasion of his seventieth birthday—is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts: * Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control. * Part II addresses algebraic systems theory, reviewing the use of algebraic systems over semirings, modules of zeros for linear multivariable systems, and zeros in linear time-delay systems. * Part III discusses advances in dynamical systems characteristics. The chapters focus on the stability of a discontinuous dynamical system, approximate decentralized fixed modes, direct optimal adaptive control, and stability of nonlinear systems with limited information. * Part IV covers engineering education and includes a unique chapter on theology and engineering, one of Sain's latest research interests. The book will be a useful reference for researchers and graduate students in systems and control, algebraic systems theory, and applied mathematics. Requiring only knowledge of undergraduate-level control and systems theory, the work may be used as a supplementary textbook in a graduate course on optimal control or algebraic systems theory.

Mathematics. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Calculus of Variations and Optimal Control; Optimization. --- Applications of Mathematics. --- Game Theory, Economics, Social and Behav. Sciences. --- Dynamical Systems and Ergodic Theory. --- Differentiable dynamical systems. --- Systems theory. --- Mathematical optimization. --- Mathématiques --- Dynamique différentiable --- Optimisation mathématique --- Nonlinear control theory. --- Stochastic control theory. --- System analysis. --- Stochastic control theory --- Nonlinear control theory --- System analysis --- Differentiable dynamical systems --- Civil & Environmental Engineering --- Operations Research --- Engineering & Applied Sciences --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Network theory --- Systems analysis --- Algebra. --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Probabilities. --- Control engineering. --- Robotics. --- Mechatronics. --- Probability Theory and Stochastic Processes. --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Network analysis --- Network science --- System theory --- Mathematical optimization --- Control theory --- Nonlinear theories --- Stochastic processes --- Distribution (Probability theory. --- Systems, Theory of --- Systems science --- Science --- Math --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- Mathematics --- Philosophy --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Engineering --- Engineering analysis --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of

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Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. The book will be ideal for a beginning graduate course in mathematical control theory, or for self study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. "This book is designed as a graduate text on the mathematical theory of deterministic control. It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory." — Bulletin of the AMS "The book is very well written from a mathematical point of view of control theory. The author deserves much credit for bringing out such a book which is a useful and welcome addition to books on the mathematics of control theory." — Control Theory and Advance Technology "At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone." — Gian-Carlo Rota, The Bulletin of Mathematics Books.

Mathematics. --- Systems Theory, Control. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Control, Robotics, Mechatronics. --- Systems theory. --- Mathematical optimization. --- Mathématiques --- Optimisation mathématique --- Control theory --- Control theory. --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Calculus of variations. --- Control engineering. --- Robotics. --- Mechatronics. --- Dynamics --- Machine theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Systems, Theory of --- Systems science --- Philosophy --- Control engineering --- Control equipment --- Engineering instruments --- Automation --- Programmable controllers --- Isoperimetrical problems --- Variations, Calculus of --- Engineering --- Engineering analysis --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Mathematics