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Real-Time Optimization of DAE Systems

  • Christof Büskens
  • Matthias Gerdts
Chapter

Abstract

We consider approaches for real-time optimization of dynamical systems governed by differential-algebraic (DAE) systems. Special attention is turned on the calculation of consistent initial values such that the DAE system is solvable.

The underlying DAE optimal control problem is solved numerically by a direct single shooting method. This method reduces the infinite dimensional optimal control problem by discretization of the control over a suitable chosen grid to a finite dimensional optimization problem.

A real-time optimization method is achieved by performing a parameter sensitivity analysis of the discretized optimal control problem, taking the calculation of consistent initial values into account.

A high dimensional and highly nonlinear example of a car’s jink is discussed to demonstrate the capabilities of the proposed methods.

Keywords

Optimal Control Problem Tyre Force Steer Wheel Angle Discretized Optimal Control Problem Hide Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    K. E. Brenan, S. L. Campbell, L. R. Petzold: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Classics In Applied Mathematics 14, SIAM, Philadelphia, (1996)Google Scholar
  2. 2.
    C. Büskens, Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy. This volume.Google Scholar
  3. 3.
    C. Büskens and H. Maurer, Sensitivity Analysis and Real-Time Optimization of Para metric Nonlinear Programming Problems. This volume.Google Scholar
  4. 4.
    C. Büskens and H. Maurer, Sensitivity Analysis and Real-Time Control of Optimal Con trol Problems Using Nonlinear Programming Methods. This volumeGoogle Scholar
  5. 5.
    C. Büskens, M. Gerdts: Numerical Solution of Optimal Control Problems with DAE Systems of Higher Index. Proceedings of the workshop “Optimalsteuerungsprobleme in der Luft- und Raumfahrt” at Greifswald, SFB 255: Transatmosphärische Flugsysteme, Munchen, (2000)Google Scholar
  6. 6.
    S. L. Campbell, C. W. Gear: The Index of General Nonlinear DAEs. Numerische Mathematik 71(1995)Google Scholar
  7. 7.
    C. W. Gear: Differential-Algebraic Equation Index Transformations. SIAM Journal on Scientific and Statistical Computing 9 (1988) 39–47MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    M. Gerdts: Numerische Methoden optimaler Steuerprozesse mit differential-algebra-ischen Gleichungssystemen hoheren Indexes und ihre Anwendungen in der Kraftfahrzeugsimulation und Mechanik. Bayreuther Mathematische Schriften 61, Bayreuth, (2001).Google Scholar
  9. 9.
    H. Hinsberger: Ein direktes Mehrzielverfahren zur Lösung von Optimalsteuerungsproblemen mit großen, differential-algebraischen Gleichungssystemen und Anwendungen aus der Verfahrenstechnik. Dissertation, Institut für Mathematik, Technische Universität Clausthal, (1997)Google Scholar
  10. 10.
    B. Leimkuhler, L. R. Petzold, C. W. Gear: Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations. SIAM Journal on Numerical Analysis 28, (1), (1991) 205–226MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    L. R. Petzold: A Description of DASSL: A Differential/Algebraic System Solver. Report Sand 82–8637, Sandia National Laboratory, Livermore, (1982)Google Scholar
  12. 12.
    H.-J. Risse: Das Fahrverhalten bei normaler Fahrzeugführung. VDI Fortschrittberichte Reihe 12: Verkehrstechnik/Fahrzeugtechnik 160 VDI-Verlag, (1991)Google Scholar
  13. 13.
    F. Uffelmann: Berechnung des Lenk- und Bremsverhaltens von Kraftfahrzeugen auf rutschiger Fahrbahn. Dissertation, Fakultät für Maschinenbau und Elektrotechnik, Tech-nische Universität Braunschweig, (1980)Google Scholar
  14. 14.
    P. Wiegner: Über den Einfluß von Blockierverhinderern auf das Fahrverhalten von Perso-nenkraftwagen bei Panikbremsungen. Dissertation, Fakultät für Maschinenbau und Elektrotechnik, Technische Universität Braunschweig, (1974)Google Scholar
  15. 15.
    A. Zomotor: Fahrwerktechnik: Fahrverhalten. Vogel Buchverlag, Stuttgart, (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christof Büskens
    • 1
  • Matthias Gerdts
    • 2
  1. 1.Lehrstuhl für IngenieurmathematikUniversität BayreuthGermany
  2. 2.Lehrstuhl für Angewandte MathematikUniversität BayreuthGermany

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