Advertisement

On the Minimum Time Problem for Dodgem Car–Like Bang–Singular Extremals

  • L. Poggiolini
  • G. Stefani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

Abstract

In this paper we analyse second order conditions for a bang–singular extremal in a class of problems including the Dodgem–car one. Moreover we state some result on optimality and structural stability whose proof will appear elsewhere.

Keywords

Quadratic Form Reference Trajectory Integral Line Pontryagin Maximum Principle Singular Control 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agrachev, A.A., Sachkov, Y.L.: Control Theory from the Geometric Viewpoint. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  2. 2.
    Agrachev, A.A., Stefani, G., Zezza, P.: An invariant second variation in optimal control. Internat. J. Control 71(5), 689–715 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Craven, B.D.: Control and optimization. Chapman & Hall (1995)Google Scholar
  4. 4.
    Felgenhauer, U.: Structural Stability Investigation of Bang-Singular-Bang Optimal Controls. Journal of Optimization Theory and Applications 152, 605–631 (2012)zbMATHCrossRefGoogle Scholar
  5. 5.
    Poggiolini, L., Stefani, G.: Sufficient optimality conditions for a bang–singular extremal in the minimum time problem. Control and Cybernetics 37(2), 469–490 (2008)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Poggiolini, L., Stefani, G.: Bang-singular-bang extremals: sufficient optimality conditions. Journal of Dynamical and Control Systems 17(4), 469–514 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishenko, E.F.: The Mathematical Theory of Optimal Processes. Wiley (1962)Google Scholar
  8. 8.
    Stefani, G., Zezza, P.: Constrained regular LQ-control problems. SIAM J. Control Optim. 35(3), 876–900 (1997)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • L. Poggiolini
    • 1
  • G. Stefani
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaUniversità degli Studi di FirenzeItaly

Personalised recommendations