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Applications to Regular and Bang-Bang Control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control

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by Nikolai P. Osmolovskii and Helmut Maurer


2012 / xviii + 382 pages / Softcover / ISBN 978-1-611972-35-1 /List Price $109.00 / SIAM Member Price $76.30 / Order Code DC24

Keywords: Pontryagin's principle, second order optimality conditions, regular and bang-bang control, numerical methods, applications


This book is devoted to the theory and applications of second-order necessary and sufficient optimality conditions in the calculus of variations and optimal control. The authors develop theory for a control problem with ordinary differential equations subject to boundary conditions of both the equality and inequality type and for mixed state-control constraints of the equality type. The book is distinctive in that

  • necessary and sufficient conditions are given in the form of no-gap conditions;
  • the theory covers broken extremals where the control has finitely many points of discontinuity; and
  • a number of numerical examples in various application areas are fully solved.

This book is suitable for researchers in calculus of variations and optimal control and researchers and engineers in optimal control applications in mechanics; mechatronics; physics; chemical, electrical, and biological engineering; and economics.

About the Author
Nikolai P. Osmolovskii is a Professor in the Department of Informatics and Applied Mathematics, Moscow State Civil Engineering University; the Mechanical Mathematics Department, Moscow State University; the Institute of Mathematics and Physics, University of Siedlce, Poland; the Systems Research Institute, Polish Academy of Science; and the Technical University of Radom, Poland. He was an Invited Professor in the Department of Applied Mathematics, University of Bayreuth, Germany (2000), and in the Centre de Mathématiques Appliquées, École Polytechnique, France (2007). His fields of research are functional analysis, calculus of variations, and optimal control theory. He has written 50 papers and four monographs.

Helmut Maurer was a Professor of Applied Mathematics at the University of Muenster (retired 2010) and has conducted research in Austria, France, Poland, Australia, and the United States. His fields of research in optimal control are control and state constraints, numerical methods, second-order sufficient conditions, sensitivity analysis, real-time control techniques, and various applications in mechanics, mechatronics, physics, biomedical and chemical engineering, and economics.

ISBN 9781611972351

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