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Applications to Regular and Bang-Bang Control

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Applications to Regular and Bang-Bang Control

Applications to Regular and Bang-Bang Control

Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control
Nikolai P. Osmolovskii, Technical University of Radom
Helmut Maurer, Westfälische Wilhelms-Universität Münster, Germany
February 2014
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Paperback
9781611972351
$125.00
USD
Paperback
    Description

    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 equality and inequality type, and for mixed state-control constraints of equality type. The book has several distinctive features: 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 areas of application are fully solved. This book will be of interest to academic researchers in calculus of variations and optimal control. It will also be a useful resource to researchers and engineers who use applications of optimal control in areas such as mechanics, mechatronics, physics, economics, or chemical, electrical, and biological engineering.

    • Second order conditions are derived as no-gap conditions
    • The theory can be applied to broken extremals (controls with finitely many points of discontinuity)
    • Several numerical examples are presented and solved in full

    Product details

    February 2014
    Paperback
    9781611972351
    390 pages
    253 × 177 × 20 mm
    0.69kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    Table of Contents

    • List of figures
    • Notation
    • Preface
    • Introduction
    • Part I. Second-Order Optimality Conditions for Broken Extremals in the Calculus of Variations:
    • 1. Abstract scheme for obtaining higher-order conditions in smooth extremal problems with constraints
    • 2. Quadratic conditions in the calculus of variations
    • 3. Quadratic conditions for optimal control problems with mixed control-state constraints problems
    • 4. Jacobi-type conditions and Riccati equation
    • Part II. Second-Order Optimality Conditions in Optimal Bang-Bang Control Problems:
    • 5. Second-order optimality conditions in optimal control
    • 6. Second-order optimality conditions for bang-bang control
    • 7. Bang-bang control and induced optimization problem
    • 8. Numerical methods for solving the induced optimization problem
    • Bibliography
    • Index.
      • Show more
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    About the authors
      Authors
    • Nikolai P. Osmolovskii , Technical University of Radom

      Nikolai Osmolovskii holds several professorships, which include positions at the University of Siedlce, the Polish Academy of Science and the Technical University of Radom. He has authored 50 research papers and four monographs.

    • Helmut Maurer , Westfälische Wilhelms-Universität Münster, Germany

      Helmut Maurer has held a professorship at the University of Münster since 1977; he retired in 2010, but remains active in many international research projects.

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