This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].
This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.
Dark secrets and the disappearances of nearly everyone he has ever loved converge in a case that leads Dek Elstrom on a trail to northern Michigan and a forgotten ice-swept island where a death raises dangerous questions about Elstrom's home in Rivertown.
This top-selling guide is the ultimate for any angler looking for new fishing spots in Colorado. The book is packed with extensive information on where to fish within Colorado's national forests, national recreation areas, state parks, and state trust lands. It includes directions to lakes and streams, detailed maps, information about governing agencies, kinds of fish you will find, and insightful comments.
Considering the course his life took, one might wonder how Zachary Taylor ever came to be elected the twelfth president of the United States. According to K. Jack Bauer, Taylor “was and remains an enigma.” He was a southerner who espoused many antisouthern causes, an aristocrat with a strong feeling for the common man, an energetic yet cautious and conservative soldier. Not an intellectual, Taylor showed little curiosity about the world around him. In this biography—the most comprehensive since Holman Hamilton’s two-volume work published forty years ago—Bauer offers a fresh appraisal of Taylor’s life and suggests that Taylor may have been neither so simple nor so nonpolitical as many historians have believed. Taylor’s sixteen months as president were marked by disputes over California statehood and the Texas–New Mexico boundary. Taylor vehemently opposed slavery extension and threatened to hang those southern hotheads who favored violence and secession as a means to protect their interests. He died just as he had begun a reorganization of his administration and a recasting of the Whig party. Balanced and judicious, forthright and unreverential, and based on thoroughgoing research, this book will be for many years the standard biography of Zachary Taylor.
Contains twelve selections by turn-of-the-century American author Jack London, including the novel "The Call of the Wild"; the short story collection "The Son of the Wolf"; and two additional tales; and includes an essay about London by Carl Sandburg.
This monograph is an introduction to optimal control theory for systems governed by vector ordinary differential equations. It is not intended as a state-of-the-art handbook for researchers. We have tried to keep two types of reader in mind: (1) mathematicians, graduate students, and advanced undergraduates in mathematics who want a concise introduction to a field which contains nontrivial interesting applications of mathematics (for example, weak convergence, convexity, and the theory of ordinary differential equations); (2) economists, applied scientists, and engineers who want to understand some of the mathematical foundations. of optimal control theory. In general, we have emphasized motivation and explanation, avoiding the "definition-axiom-theorem-proof" approach. We make use of a large number of examples, especially one simple canonical example which we carry through the entire book. In proving theorems, we often just prove the simplest case, then state the more general results which can be proved. Many of the more difficult topics are discussed in the "Notes" sections at the end of chapters and several major proofs are in the Appendices. We feel that a solid understanding of basic facts is best attained by at first avoiding excessive generality. We have not tried to give an exhaustive list of references, preferring to refer the reader to existing books or papers with extensive bibliographies. References are given by author's name and the year of publication, e.g., Waltman [1974].
This book presents results on the geometric/topological structure of the solution set S of an initial-value problem x(t) = f(t, x(t)), x(0) =xo, when f is a continuous function with values in an infinite-dimensional space. A comprehensive survey of existence results and the properties of S, e.g. when S is a connected set, a retract, an acyclic set, is presented. The authors also survey results onthe properties of S for initial-value problems involving differential inclusions, and for boundary-value problems. This book will be of particular interest to researchers in ordinary and partial differential equations and some workers in control theory.
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