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Invariant Approximations of the Minimal Robust Positively Invariant Set via Finite Time Aumann Integrals

Author(s):

Sasa V. Rakovic, K. I. Kouramas
Conference/Journal:

IEEE Conference on Decision and Control
Abstract:

This paper provides results on the minimal robust positively invariant set and its robust positively invariant approximations of an asymptotically stable, continuous-time, linear time-invariant system. The minimal robust positively invariant set is characterized as an infinite time Aumann Integral. A novel family of robust positively invariant sets, defined as a simple scaling of a finite time Aumann Integral, is characterized. Adequate members of this family are robust positively invariant sets and are arbitrarily close outer approximations of the minimal robust positively invariant set. Conditions are given that allow one to specify a priori the accuracy of the approximation. A practical result, based on the optimal control theory, for the construction of safe polytopic sets is also provided. Computational procedures are briefly discussed and connection with the recent methods for the reachability computations is pointed out. Some simple and illustrative examples are provided.

Further Information
Year:

2007
Type of Publication:

(01)Article
Supervisor:



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% Autogenerated BibTeX entry
@InProceedings { RakKou:2007:IFA_2838,
    author={Sasa V. Rakovic and K. I. Kouramas},
    title={{Invariant Approximations of the Minimal Robust Positively
	  Invariant Set via Finite Time Aumann Integrals}},
    booktitle={IEEE Conference on Decision and Control},
    pages={},
    year={2007},
    address={},
    month=dec,
    url={http://control.ee.ethz.ch/index.cgi?page=publications;action=details;id=2838}
}
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