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Liapunov reachability and optimization in control

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Abstract

In this paper, we find sufficient conditions that do not rely upon any Liapunov stability results for the reachability of the target set by an admissible control from ana priori specified set of states. The conditions found are less restrictive than those obtained by Sticht, Vincent, and Schultz in Ref. 1.

For control problems with specific integral performance index, we also show that, if a quantitative Liapunov function for optimization exists, then it may also serve as a qualitative Liapunov function ensuring the reachability of the target. The results are illustrated by examples.

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References

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Authors and Affiliations

  1. Mathematics Department, University of Queensland, Brisbane, Queensland, Australia

    R. J. Stoner (Senior Tutor)

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  1. R. J. Stoner
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Communicated by G. Leitmann

The author is indebted to Prof. J. M. Skowronski and Prof. P. Seibert for their useful comments and discussions.

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Stoner, R.J. Liapunov reachability and optimization in control. J Optim Theory Appl 39, 403–416 (1983). https://doi.org/10.1007/BF00934546

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