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Reachability Analysis via Invariant Sets


Sasa V. Rakovic


The talk is concerned with the utilization of invariant sets in reachability analysis. We discuss a version of the reachability analysis problem and we propose a method that allows for a relatively efficient computation of the inner and outer approximations of the exact reach sets/tubes. In fact, we show how to obtain ``on-line'' inner and outer estimates of the exact reach sets/tubes of an `n` dimensional uncertain linear discrete time system from a difference equation of an `n+2' dimensional deterministic system. The computational simplification is obtained by exploiting a particular parameterization of the inner and outer bounding tubes with invariant tube cross section (constructed off-line). We give an illustrative example demonstrating that the proposed method can handle the ``wrapping effect'' in contrast to the methods in the literature based on using simple approximating sets such as zonotopes, polytopes, ellipsoids.

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