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The mathematical theory of control became a ?eld of study half a century ago in attempts to clarify and organize some challenging practical problems and the methods used to solve them. It is known for the breadth of the mathematics it uses and its cross-disciplinary vigor. Its literature, which can befoundinSection93ofMathematicalReviews,wasatonetimedominatedby the theory of linear control systems, which mathematically are described by linear di?erential equations forced by additive control inputs. That theory led to well-regarded numerical and symbolic computational packages for control analysis and design. Nonlinear control problems are also important; in these either the - derlying dynamical system is nonlinear or the controls are applied in a n- additiveway.Thelastfourdecadeshaveseenthedevelopmentoftheoretical work on nonlinear control problems based on di?erential manifold theory, nonlinear analysis, and several other mathematical disciplines. Many of the problems that had been solved in linear control theory, plus others that are new and distinctly nonlinear, have been addressed; some resulting general de?nitions and theorems are adapted in this book to the bilinear case.
The purpose of this book is to present a self-contained description of the fun damentals of the theory of nonlinear control systems, with special emphasis on the differential geometric approach. The book is intended as a graduate text as weil as a reference to scientists and engineers involved in the analysis and design of feedback systems. The first version of this book was written in 1983, while I was teach ing at the Department of Systems Science and Mathematics at Washington University in St. Louis. This new edition integrates my subsequent teaching experience gained at the University of Illinois in Urbana-Champaign in 1987, at the Carl-Cranz Gesellschaft in Oberpfaffenhofen in 1987, at the University of California in Berkeley in 1988. In addition to a major rearrangement of the last two Chapters of the first version, this new edition incorporates two additional Chapters at a more elementary level and an exposition of some relevant research findings which have occurred since 1985.
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Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
The volume contains papers based on lectures delivered during the school "Per spectives in Control Theory" held in Sielpia, Poland on September 19-24, 1988. The aim of the school was to give the state-of-the-art presentation of recent achievements as weH as perspectives in such fields of control theory as optimal control and optimization, linear systems, and nonlinear systems. Accordingly, the volume includes survey papers together with presentations of some recent results. The special emphasis is put on: - nonlinear systems (algebraic and geometric methods), - optimal control and optimization (general problems, distributed parameter systems), - linear systems (linear-quadratic problem, robu...
"We should all be cooking like Adeena Sussman." --The Wall Street Journal "Sababa is a breath of fresh, sunny air." --The New York Times In an Israeli cookbook as personal as it is global, Adeena Sussman celebrates the tableau of flavors the region has to offer, in all its staggering and delicious variety In Hebrew (derived from the original Arabic), sababa means "everything is awesome," and it's this sunny spirit with which the American food writer and expat Adeena Sussman cooks and dreams up meals in her Tel Aviv kitchen. Every morning, Sussman makes her way through the bustling stalls of Shuk Hacarmel, her local market, which sells irresistibly fresh ingredients and tempting snacks--juicy...
Reading Talmudic Sources as Arguments: A New Interpretive Approach elucidates the unique characteristics of Talmudic discourse culture. Approaching Talmudic literature from a linguistic perspective, the book shows the extensive and hidden ways in which later rabbis used early formulations. Applying Quentin Skinner's interpretive question “What was the author doing in composing the text in this particular way?" to Talmudic literature reveals that Talmudic debate is not only about ideas, concepts and laws but also about the latter's connection to pre-existing formulations. These early traditions, rather than only being accepted or not, are used by later generations to build their own arguments. The book articulates the function of tradition at the time that Rabbinic Judaism was forged.
Born at the beginning of the 20th century, Raphael Ignatius Phoenix is determined to take his own life as the new millennium begins and he turns a hundred years old. But before he ends it all, he wants to get his affairs in order, and that includes making sense of his own life. He decides to write it down, remembering the experiences, the myriad encounters and, of course, the ten murders he committed along the way...
This volume on mathematical control theory contains high quality articles covering the broad range of this field. The internationally renowned authors provide an overview of many different aspects of control theory, offering a historical perspective while bringing the reader up to the very forefront of current research.