2002/02/07 by Ravi, D., Shyamasundar, R. K.
#D2.2 #F3 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Software Engineering (cs.SE)
paper · doi:10.48550/arxiv.cs/0202006
One of the most important problems in hybrid systems is the \em reachability problem. The reachability problem has been shown to be undecidable even for a subclass of \em linear hybrid systems. In view of this, the main focus in the area of hybrid systems has been to find \em effective semi-decision procedures for this problem. Such an algorithmic approach involves finding methods of computation and representation of reach sets of the continuous variables within a discrete state of a hybrid system. In this paper, after presenting a brief introduction to hybrid systems and reachability problem, we propose a computational method for obtaining the reach sets of continuous variables in a hybrid system. In addition to this, we also describe a new algorithm to over-approximate with polyhedra the reach sets of the continuous variables with linear dynamics and polyhedral initial set. We illustrate these algorithms with typical interesting examples.