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On the Set of Trajectories of the Control Systems with Limited Control Resources

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Curves and Surfaces (Curves and Surfaces 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9213))

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Abstract

The set of trajectories of the control system with limited control resources is studied. It is assumed that the behavior of the system is described by a Volterra type integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector. The closed ball of the space \(L_p\) \((p>1)\) with radius \(\mu \) and centered at the origin, is chosen as the set of admissible control functions. It is proved that for each fixed p the set of trajectories is Lipschitz continuous with respect to \(\mu \) and for each fixed \(\mu \) is continuous with respect to p. The upper evaluation for the diameter of the set of trajectories is given.

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Author information

Authors and Affiliations

  1. Mathematics Department, Anadolu University, 26470, Eskisehir, Turkey

    Nesir Huseyin, Anar Huseyin & Khalik G. Guseinov

Authors
  1. Nesir Huseyin
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  2. Anar Huseyin
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  3. Khalik G. Guseinov
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Corresponding author

Correspondence to Khalik G. Guseinov .

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. École Normale Supérieure, Paris, France

    Albert Cohen

  3. Arts Et Metiers ParisTech Lab de Sciences de l'Information, Paris, France

    Olivier Gibaru

  4. INSA de Rouen, LMI, Saint-Étienne-du-Rouvray, France

    Christian Gout

  5. Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche

  6. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Huseyin, N., Huseyin, A., Guseinov, K.G. (2015). On the Set of Trajectories of the Control Systems with Limited Control Resources. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_21

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  • DOI: https://doi.org/10.1007/978-3-319-22804-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22803-7

  • Online ISBN: 978-3-319-22804-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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