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Computational complexity of μ calculation

Braatz, Richard D. and Young, Peter M. and Doyle, John C. and Morari, Manfred (1993) Computational complexity of μ calculation. In: 1993 American Control Conference. IEEE , Piscataway, NJ, pp. 1682-1683. ISBN 0-7803-0860-3.

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The structured singular value μ measures the robustness of uncertain Systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems.

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Doyle, John C.0000-0002-1828-2486
Additional Information:© 1993 IEEE. Supported by the Fannie and John Hertz Foundation The authors thank Professor John Tsitsiklis at MIT for his comments.
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Fannie and John Hertz FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20190320-132001216
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Official Citation:R. D. Braatz, P. M. Young, J. C. Doyle and M. Morari, "Computational complexity of μ calculation," 1993 American Control Conference, San Francisco, CA, USA, 1993, pp. 1682-1683. doi: 10.23919/ACC.1993.4793162
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93998
Deposited By: Tony Diaz
Deposited On:20 Mar 2019 20:46
Last Modified:16 Nov 2021 17:02

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