An introductory text on the analysis, control, and estimation of nonlinear systems, appropriate for advanced undergraduate and graduate students
Hardcover
ISBN: 9780691240480
Published (US):Jun 27, 2023
Pages:552
Size:7 x 10 in.
166 b/w illus. 2 tables.
This self-contained and accessible introduction to the concepts and techniques used for nonlinear feedback systems offers a holistic treatment suitable for use in both advanced undergraduate and graduate courses; students need only some familiarity with differential equations and linear algebra to understand the material presented. The text begins with an overview of stability and Lyapunov methods for nonlinear systems, with Lyapunov’s second method revisited throughout the book as a connective thread. Other introductory chapters cover linear systems, frequency domain methods, and discrete-time systems. Building on this background material, the book provides a broad introduction to the basic ideas underpinning major themes of research in nonlinear control, including input-to-state stability, sliding mode control, adaptive control, feedback linearization, and robust output regulation. Chapters also cover observer design and estimation for nonlinear systems. The text is notable for its coverage of nonlinear model predictive control and its introduction to the use of linear matrix inequalities and semidefinite programming coupled with their use in modern antiwindup designs.
? First text on nonlinear control appropriate for undergraduates
? Suitable both for students preparing for rigorous graduate study and for those entering technical fields outside of academia
? Unique in its coverage of recent research topics
? Pedagogical features including extensive chapter summaries, examples, and appendixes with definitions, results, and MATLAB applications
Hardcover
Paperback
ISBN: 9780691242040
Jan 3, 2023
Pages: 528
Size: 7 x 10 in. 36 b/w illus.
Plato’s Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincare, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naive set theory and the revived axiomatic method?debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.
Plato’s Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
A pioneering new nonlinear approach to a fundamental question in algebraic geometry
Series: Annals of Mathematics Studies
Hardcover
SBN: 9780691246819
Paperback
ISBN: 9780691246802
Published: Jul 25, 2023
Pages: 240
Size: 6.13 x 9.25 in.
Illus: 4 b/w illus.
One of the crowning achievements of nineteenth-century mathematics was the proof that the geometry of lines in space uniquely determines the Cartesian coordinates, up to a linear ambiguity. What Determines an Algebraic Variety? develops a nonlinear version of this theory, offering the first nonlinear generalization of the seminal work of Veblen and Young in a century. While the book uses cutting-edge techniques, the statements of its theorems would have been understandable a century ago; despite this, the results are totally unexpected. Putting geometry first in algebraic geometry, the book provides a new perspective on a classical theorem of fundamental importance to a wide range of fields in mathematics.
Starting with basic observations, the book shows how to read off various properties of a variety from its geometry. The results get stronger as the dimension increases. The main result then says that a normal projective variety of dimension at least 4 over a field of characteristic 0 is completely determined by its Zariski topological space. There are many open questions in dimensions 2 and 3, and in positive characteristic.