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Limit Behavior of Reachable Sets of Linear Time-Invariant Systems with Integral Bounds on Control

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Abstract

In this paper, a linear dynamic system is considered under L p -constraint on control. We establish the existence of the limit shape of reachable sets as time goes to infinity. Asymptotic formulas are obtained for reachable sets and their shapes. The results throw a bridge between the cases of geometric bounds on control and constraints on the total impulse of control, and create a unified picture of the structure of the limit shapes of reachable sets.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia

    Elena Goncharova

  2. Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    Alexander Ovseevich

Authors
  1. Elena Goncharova
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  2. Alexander Ovseevich
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Corresponding author

Correspondence to Elena Goncharova.

Additional information

Communicated by Felix L. Chernousko.

The work was partially supported by the Russian Foundation for Basic Research under grant 11-08-00435.

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Goncharova, E., Ovseevich, A. Limit Behavior of Reachable Sets of Linear Time-Invariant Systems with Integral Bounds on Control. J Optim Theory Appl 157, 400–415 (2013). https://doi.org/10.1007/s10957-012-0198-z

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  • DOI: https://doi.org/10.1007/s10957-012-0198-z

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