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Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control

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Abstract

This paper derives a feedback controlf(t), ‖f(t)‖E≦r,r>0, which forces the infinite-dimensional control systemdu/dt=Au+Bf, u(0)=u o ≠H to have the asymptotic behavioru(t)→0 ast→∞ inH. HereA is the infinitesimal generator of aC o semigroup of contractionse At on a real Hilbert spaceH andB is a bounded linear operator mapping a Hilbert space of controlsE intoH. An application to the boundary feedback control of a vibrating beam is provided in detail and an application to the stabilization of the NASA Spacecraft Control Laboratory is sketched.

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Authors and Affiliations

  1. Center for the Mathematical Sciences, University of Wisconsin-Madison, 53705, Madison, Wisconsin, USA

    Marshall Slemrod (Erna and Jakob Michael Visiting Professor)

  2. Weizmann Institute of Science, Rehovot, Israel

    Marshall Slemrod (Erna and Jakob Michael Visiting Professor)

Authors
  1. Marshall Slemrod
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Additional information

This research was sponsored in part by the Air Force Office of Scientific Research, Air Force Systems Command, USAF Contract/Grants AFOSR 81-0172 and AFOSR 87-0315.

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Slemrod, M. Feedback stabilization of a linear control system in Hilbert space with ana priori bounded control. Math. Control Signal Systems 2, 265–285 (1989). https://doi.org/10.1007/BF02551387

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  • DOI: https://doi.org/10.1007/BF02551387

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