Some decidable results on reachability of solvable systems

Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples.Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples