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

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Large-Scale Scientific Computing (LSSC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7116))

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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.

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References

  1. Agrachev, A.A., Sachkov, Y.L.: Control Theory from the Geometric Viewpoint. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  2. Agrachev, A.A., Stefani, G., Zezza, P.: An invariant second variation in optimal control. Internat. J. Control 71(5), 689–715 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Craven, B.D.: Control and optimization. Chapman & Hall (1995)

    Google Scholar 

  4. Felgenhauer, U.: Structural Stability Investigation of Bang-Singular-Bang Optimal Controls. Journal of Optimization Theory and Applications 152, 605–631 (2012)

    Article  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  6. Poggiolini, L., Stefani, G.: Bang-singular-bang extremals: sufficient optimality conditions. Journal of Dynamical and Control Systems 17(4), 469–514 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishenko, E.F.: The Mathematical Theory of Optimal Processes. Wiley (1962)

    Google Scholar 

  8. Stefani, G., Zezza, P.: Constrained regular LQ-control problems. SIAM J. Control Optim. 35(3), 876–900 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Poggiolini, L., Stefani, G. (2012). On the Minimum Time Problem for Dodgem Car–Like Bang–Singular Extremals. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-29843-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29842-4

  • Online ISBN: 978-3-642-29843-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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