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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


Part of Advances in Design and Control

  • Date Published: February 2014
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9781611972351

£ 74.99

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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About the Authors
  • 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
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    Product details

    • Date Published: February 2014
    • format: Paperback
    • isbn: 9781611972351
    • length: 390 pages
    • dimensions: 253 x 177 x 20 mm
    • weight: 0.69kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    List of figures
    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

  • 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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