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Approximate Reachability Analysis Using Homothety and Invariance

In this talk we discuss a method for approximate reachability, for linear discrete time systems, based on homothety and set invariance. The proposed method utilizes two particular families of sets, more precisely their members, and particular forms of the approximation maps to obtain simple inner and outer approximate reachable sets/tubes. The resulting set–dynamics, induced by the uncertainty set, the underlying dynamics in the state space and the approximation maps, are restricted to these particular families of sets and under standard assumptions yield bounded and convergent approximate reachable sets/tubes. The proposed method is computationally (relatively) simple and does not suffer from the so–called “wrapping effect” but in contrary provides improving inner and outer estimates of the exact reachable sets. We also discuss an exceptional case when the Hausdorff distance between the inner and outer approximate reachable sets converges to zero in the limit.

Type of Seminar:
IfA Seminar
Mirko Fiacchini
May 09, 2008   11:00

Contact Person:

Sasa V. Rakovic
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