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Small-Time Reachable Sets of Linear Systems with Integral Control Constraints: Birth of the Shape of a Reachable Set

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Abstract

The paper is concerned with small-time reachable sets of a linear dynamical system under integral constraints on control. The main result is the existence of a limit shape of the reachable sets as time tends to zero. A precise estimate for the rate of convergence is given.

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Notes

  1. We thank an anonymous reviewer for drawing our attention to these works.

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Acknowledgments

This work was partially supported by the Russian Foundation for Basic Research, Grants 14-08-00606, 14-01-00476, 13-08-00441. We are grateful to anonymous referees for providing insightful comments and suggesting additional bibliography.

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Correspondence to Elena Goncharova.

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Communicated by Felix L. Chernousko.

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Goncharova, E., Ovseevich, A. Small-Time Reachable Sets of Linear Systems with Integral Control Constraints: Birth of the Shape of a Reachable Set. J Optim Theory Appl 168, 615–624 (2016). https://doi.org/10.1007/s10957-015-0754-4

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  • DOI: https://doi.org/10.1007/s10957-015-0754-4

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