Probabilistic Robustness Radii with <i>n</i>:th Order Convex Distributions - Volume 6 Number 4 (Aug. 2016) - ijmo
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General Information
Prof. Adrian Olaru
University Politehnica of Bucharest, Romania
I'm happy to take on the position of editor in chief of IJMO. It's a journal that shows promise of becoming a recognized journal in the area of modelling and optimization. I'll work together with the editors to help it progress.
IJMO 2016 Vol.6(4): 211-218 ISSN: 2010-3697
DOI: 10.7763/IJMO.2016.V6.529

Probabilistic Robustness Radii with n:th Order Convex Distributions

Ilmari Kangasniemi and Juha-Pekka Nikkarila
Abstract—We analyze a probabilistic variation on the classic robustness radius. Instead of measuring the distance to the closest destabilizing state, we look at a set of probability distributions around our initial state. The probabilistic radius is the radius of the largest sphere, for which none of the distributions supported within it takes the expected values of system parameters outside a prescribed set. We show that when the set of acceptable parameter values is closed and convex, the radius for the family of distributions which are nondecreasing with respect to distance reduces to the same radius for uniform distributions. We generalize this result for distributions of higher order convexity or concavity with respect to distance, obtaining an equal radius using a simple family of polynomials.

Index Terms—Robustness radii, distributional robustness, decision analysis, control theory, aircraft control.

I. Kangasniemi and J. P. Nikkarila are with the University of Helsinki, They are also with Finnish Defence Forces Research Agency, P.O.Box 10, FI-11311 Riihimäki, Finland (e-mail:,


Cite: Ilmari Kangasniemi and Juha-Pekka Nikkarila, "Probabilistic Robustness Radii with n :th Order Convex Distributions," International Journal of Modeling and Optimization vol. 6, no. 4, pp. 211-218, 2016.

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