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Optimization and Engineering
Published in: Optimization and Engineering 4/2015

01-12-2015

Ellipsoidal bounds on state trajectories for discrete-time systems with linear fractional uncertainties

Authors: Masako Kishida, Richard D. Braatz

Published in: Optimization and Engineering | Issue 4/2015

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Abstract

Computation of exact ellipsoidal bounds on the state trajectories of discrete-time linear systems that have time-varying or time-invariant linear fractional parameter uncertainties and ellipsoidal uncertainty in the initial state is known to be NP-hard. This paper proposes three algorithms to compute ellipsoidal bounds on such a state trajectory set and discusses the tradeoffs between computational complexity and conservatism of the algorithms. The approach employs linear matrix inequalities to determine an initial estimate of the ellipsoid that is refined by the subsequent application of the skewed structured singular value \(\nu \). Numerical examples are used to illustrate the application of the proposed algorithms and to compare the differences between them, where small conservatism for the tightest bounds is observed.
previous article Constrained problem formulations for power optimization of aircraft electro-thermal anti-icing systems
next article A new algorithm using front prediction and NSGA-II for solving two and three-objective optimization problems

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Footnotes
1
Alternative objectives, such as minimizing the trace as in El Ghaoui and Calafiore (1999), can be addressed by the algorithms in this paper by slightly modifying the first step of the LMI formulation.
 
2
This derivation is simpler than an equivalent LMI derived elsewhere (El Ghaoui and Calafiore 1999).
 
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Metadata
Title
Ellipsoidal bounds on state trajectories for discrete-time systems with linear fractional uncertainties
Authors
Masako Kishida
Richard D. Braatz
Publication date
01-12-2015
Publisher
Springer US
Published in
Optimization and Engineering / Issue 4/2015
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI
https://doi.org/10.1007/s11081-014-9255-9

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