Approximate Reachability for Linear Systems
We describe new techniques to construct, and subsequently refine, over-approximations of the reachability sets for linear dynamical systems. Our approach extracts information from real eigenvectors and more generally, from certain vectors in the primary decomposition, to generate suitable invariants of the system and can be used in conjunction with other reachability computation methods. We also describe experimental results from using this technique inside the qualitative abstraction tool , where it helps to generate refined abstractions of hybrid systems with linear continuous dynamics. We illustrate this on a collision-avoidance example from automobile cruise control problem, which was handled completely automatically by our tool.
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