Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems

Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems In this paper, a new approach to worst-case simulation of discrete linear time- invariant interval dynamic systems is proposed. For stable systems, the new approach solves the problem of worst-case simulation by determining the interval hull enclosing the system states region at every iteration through optimisation. The originality of this approach is that it maintains time-invariant parametric uncertainties during the simulation process. Several previous algorithms have considered the case of parametric time-varying uncertainties (El Ghauoi, L., Calafiore, G.: Worst-Case Simulation of Uncertain Systems, in: Garulli, A., Tesi, A., and Vicino, A. (eds), Robustness in Identification and Control, Springer, London, 1999). However, Cuguer' o (Avoiding Possible Instability in Robust Simulation of Stable Parametric Uncertain Time-Invariant Systems, in: Proceedings of 40th Conference on Decision and Control, Florida, 2001) has presented possible instability problems when simulating a time-invariant uncertain system as if it were time-varying, this result being the motivation for the approach proposed in this paper. The optimisation problem associated with the approach proposed must be solved globally in order to guarantee that the minimum volume box enclosing the region of system states has been derived. In this paper, a global optimisation algorithm based on an interval branch and bound strategy is proposed. Finally, two real application examples are used to test the performance of the approach proposed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1024666428387
Publisher site
See Article on Publisher Site

Abstract

In this paper, a new approach to worst-case simulation of discrete linear time- invariant interval dynamic systems is proposed. For stable systems, the new approach solves the problem of worst-case simulation by determining the interval hull enclosing the system states region at every iteration through optimisation. The originality of this approach is that it maintains time-invariant parametric uncertainties during the simulation process. Several previous algorithms have considered the case of parametric time-varying uncertainties (El Ghauoi, L., Calafiore, G.: Worst-Case Simulation of Uncertain Systems, in: Garulli, A., Tesi, A., and Vicino, A. (eds), Robustness in Identification and Control, Springer, London, 1999). However, Cuguer' o (Avoiding Possible Instability in Robust Simulation of Stable Parametric Uncertain Time-Invariant Systems, in: Proceedings of 40th Conference on Decision and Control, Florida, 2001) has presented possible instability problems when simulating a time-invariant uncertain system as if it were time-varying, this result being the motivation for the approach proposed in this paper. The optimisation problem associated with the approach proposed must be solved globally in order to guarantee that the minimum volume box enclosing the region of system states has been derived. In this paper, a global optimisation algorithm based on an interval branch and bound strategy is proposed. Finally, two real application examples are used to test the performance of the approach proposed.

Journal

Reliable ComputingSpringer Journals

Published: Oct 4, 2004

References

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