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Numerical Methods for Optimal Control Problems

  • Book
  • © 2018

Overview

Editors:
  1. Maurizio Falcone

    1. Department of Mathematics, Sapienza University of Rome, Roma, Italy

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  2. Roberto Ferretti

    1. Department of Mathematics & Physics, Roma Tre University, Rome, Italy

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  3. Lars Grüne

    1. Mathematical Institut, Universität Bayreuth, Bayreuth, Germany

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  4. William M. McEneaney

    1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, USA

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  • Presents recent mathematical methods for optimal control problems and their applications
  • Provides rigorous mathematical results
  • Offers several hints on numerical methods and on the construction of efficient algorithms

Part of the book series: Springer INdAM Series (SINDAMS, volume 29)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. A Hamilton-Jacobi-Bellman Approach for the Numerical Computation of Probabilistic State Constrained Reachable Sets

    • Mohamed Assellaou, Athena Picarelli
    Pages 1-22

  3. An Iterative Solution Approach for a Bi-level Optimization Problem for Congestion Avoidance on Road Networks

    • Andreas Britzelmeier, Alberto De Marchi, Matthias Gerdts
    Pages 23-38

  4. Computation of Optimal Trajectories for Delay Systems: An Optimize-Then-Discretize Strategy for General-Purpose NLP Solvers

    • Simone Cacace, Roberto Ferretti, Zahra Rafiei
    Pages 39-62

  5. POD-Based Economic Optimal Control of Heat-Convection Phenomena

    • Luca Mechelli, Stefan Volkwein
    Pages 63-87

  6. Order Reduction Approaches for the Algebraic Riccati Equation and the LQR Problem

    • Alessandro Alla, Valeria Simoncini
    Pages 89-109

  7. Fractional PDE Constrained Optimization: Box and Sparse Constrained Problems

    • Fabio Durastante, Stefano Cipolla
    Pages 111-135

  8. Control, Shape, and Topological Derivatives via Minimax Differentiability of Lagrangians

    • Michel C. Delfour
    Pages 137-164

  9. Minimum Energy Estimation Applied to the Lorenz Attractor

    • Arthur J. Krener
    Pages 165-182

  10. Probabilistic Max-Plus Schemes for Solving Hamilton-Jacobi-Bellman Equations

    • Marianne Akian, Eric Fodjo
    Pages 183-209

  11. An Adaptive Max-Plus Eigenvector Method for Continuous Time Optimal Control Problems

    • Peter M. Dower
    Pages 211-240

  12. Diffusion Process Representations for a Scalar-Field Schrödinger Equation Solution in Rotating Coordinates

    • William M. McEneaney, Ruobing Zhao
    Pages 241-268
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Keywords

About this book

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games  and their applications.


Editors and Affiliations

  • Department of Mathematics, Sapienza University of Rome, Roma, Italy

    Maurizio Falcone

  • Department of Mathematics & Physics, Roma Tre University, Rome, Italy

    Roberto Ferretti

  • Mathematical Institut, Universität Bayreuth, Bayreuth, Germany

    Lars Grüne

  • Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, USA

    William M. McEneaney

About the editors

Maurizio Falcone is Professor of Numerical Analysis at the University of Rome "La Sapienza" since 2001.   He held visiting positions at several institutions including ENSTA (Paris), the IMA (Minneapolis), Paris 6 and 7, the Russian Academy of Sciences (Moscow and Ekaterinburg) and UCLA. He serves as associate editor for the journal "Dynamic Games and Applications" and  has authored a monograph and about 80 papers in international journals.
His research interests include numerical analysis, control theory and differential games.

Roberto Ferretti is Associate Professor of Numerical Analysis at Roma Tre University since 2001. He has been an invited professor in UCLA (USA), Universitet Goroda Pereslavlya (Russia), ENSTA-Paristech and IRMA (France), TU Munich (Germany) and UP Madrid (Spain). He has authored a monograph and more than 40 papers on international journals/volumes, in topics ranging from semi-Lagrangian schemes to optimal control, levelset methods, image processing and computational fluid Dynamics.

Lars Grüne is Professor for Applied Mathematics at the University of Bayreuth, Germany. He obtained his Ph.D. from the University of Augsburg in 1996 and his habilitation from Goethe University in Frankfurt/M in 2001. He held visiting positions at the Sapienza in Rome (Italy) and at the University of Newcastle (Australia) and is Editor-in-Chief of the journal Mathematics of Control, Signals and Systems. His research interests lie in the areas of mathematical systems theory and optimal control.

William M. McEneaney received B.S. and M.S. degrees in Mathematics from Rensselaer Polytechnic Inst., followed by M.S. and Ph.D. degrees in Applied Mathematics from Brown Univ. He has held academic positions at Carnegie Mellon Univ. and North Carolina State Univ., prior to his current appointment at Univ. of California, San Diego. His non-academic positions have included Jet Propulsion Laboratory and AirForce Office of Scientific Research. His interests include Stochastic Control and Games, Max-Plus Algebraic Numerical Methods, and the Principle of Stationary Action.

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