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\iteman{io-port 01065130}
\itemau{Asarin, Eugene; Maler, Oded; Pnueli, Amir}
\itemti{Reachability analysis of dynamical systems having piecewise-constant derivatives.}
\itemso{Theor. Comput. Sci. 138, No.1, 35-65 (1995).}
\itemab
Summary: We consider a class of hybrid systems, namely dynamical systems with piecewise-constant derivatives (PCD systems). Such systems consist of a partition of the Euclidean space into a finite set of polyhedral sets (regions). Within each region the dynamics is defined by a constant vector field, hence discrete transitions occur only on the boundaries between regions where the trajectories change their direction. With respect to such systems we investigate the reachability question: Given an effective description of the systems and of two polyhedral subsets $P$ and $Q$ of the state-space, is there a trajectory starting at some $x\in P$ and reaching some point in $Q$? Our main results are a decision procedure for two-dimensional systems, and an undecidability result for three or more dimensions.
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\itemcc{}
\itemut{PCD systems; dynamical systems; piecewise-constant derivatives; reachability}
\itemli{doi:10.1016/0304-3975(94)00228-B}
\end