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Optimal Control Theory and its Applications pp 197–218Cite as

On Reachable Sets

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 106))

Abstract

The main purpose of this paper is to study the geometric properties of the reachable set R of autonomous linear control systems

$$ \dot x\, = \,Ax\, - \,u\,,\quad u(t)\, \in \,U,$$
((1))

where A is a real n×n-matrix and U is a constraint set in Rn.

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References

  1. Filippov, A.F., On certain questions in the theory of optimal control, SIAM J. Control 1, (1), (1962), 76–84.

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  2. Hajek, O., Terminal manifold and switching locus. Math. System Theory, 6 (1973), 289–301.

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  3. Hajek, O., Geometric theory of time optimal control. SIAM J. Control 9 (1971), 339–350.

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  4. Hermes, H. and LaSalle, J.P., Functional Analysis and Time Optimal Control. Academic Press, New York, 1969.

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  5. Lee, E.B. and Markus, L., Foundation of Optimal Control Theory. Wiley, New York, 1969.

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Author information

Authors and Affiliations

  1. Case Western Reserve University, USA

    Feng-Hsia Hsu

Authors
  1. Feng-Hsia Hsu
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Editor information

Editors and Affiliations

  1. Mathematics Department, Queen’s University, Kingston, Ontario, Canada

    Bruce J. Kirby

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© 1974 Springer-Verlag Berlin · Heidelberg

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Cite this paper

Hsu, FH. (1974). On Reachable Sets. In: Kirby, B.J. (eds) Optimal Control Theory and its Applications. Lecture Notes in Economics and Mathematical Systems, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48290-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-48290-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07026-9

  • Online ISBN: 978-3-642-48290-8

  • eBook Packages: Springer Book Archive

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