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Practical stabilizability of uncertain dynamical systems: Application to robotic tracking

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Abstract

The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to σ. The theory is illustrated in a numerical example of a robot with two degrees of freedom.

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Author information

Author notes

  1. M. Corless (Research Assistant)

    Present address: School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana

Authors and Affiliations

  1. School of Mathematics, University of Bath, Bath, England

    E. P. Ryan (Reader)

  2. Department of Mechanical Engineering, University of California, Berkeley, California

    G. Leitmann (Professor) & M. Corless (Research Assistant)

Authors
  1. E. P. Ryan
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  2. G. Leitmann
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  3. M. Corless
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Additional information

This paper is based on research supported by the National Science Foundation and the Air Force Office of Scientific Research under Grant ECS-8210324 and by the UK Science and Engineering Research Council under Grants GR/B/32047 and GR/C/43658. This research was carried out, in part, while G. Leitmann was the recipient of a US Senior Scientist Award of the Alexander von Humboldt Foundation.

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Ryan, E.P., Leitmann, G. & Corless, M. Practical stabilizability of uncertain dynamical systems: Application to robotic tracking. J Optim Theory Appl 47, 235–252 (1985). https://doi.org/10.1007/BF00940771

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