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Sufficient Conditions for Small Time Local Attainability for a Class of Control Systems

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Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

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Abstract

We deal with the problem of small time local attainability (STLA) for nonlinear finite-dimensional time-continuous control systems. More precisely, given a nonlinear system \(\dot{x}(t)=f(t,x(t),u(t))\), \(u(t)\in U\), possibly subjected to state constraints \(x(t)\in \varOmega \) and a closed set S, our aim is to provide sufficient conditions to steer to S every point of a suitable neighborhood of S along admissible trajectories of the system, respecting the constraints, and giving also an upper estimate of the minimum time needed for each point near S to reach S.

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References

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Acknowledgements

A. Marigonda—The first author has been supported by INdAM - GNAMPA Project 2015: Set-valued Analysis and Optimal Transportation Theory Methods in Deterministic and Stochastics Models of Financial Markets with Transaction Costs.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Strada Le Grazie, 15, 37134, Verona, Italy

    Antonio Marigonda

  2. Department of Pure and Applied Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Thuy Thi Le

Authors
  1. Antonio Marigonda
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  2. Thuy Thi Le
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Corresponding author

Correspondence to Antonio Marigonda .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Marigonda, A., Le, T.T. (2015). Sufficient Conditions for Small Time Local Attainability for a Class of Control Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-26520-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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