Some decidable results on reachability of solvable systems

Abstract

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.

Keywords:

• reachability analysis
• solvable mappings
• nonlinear systems
• hybrid systems
• symbolic computation
• decision procedures

Acknowledgements

We thank Professors Lu Yang, Chaochen Zhou, Bican Xia, and Naijun Zhan for their beneficial discussions on our work. We are also grateful to the anonymous reviewers whose insightful comments helped us to improve the presentation. This work is supported in part by NSFC (No. 11071273 & No. 91118007), SRFDP (No. 20110076120015), and Shanghai Municipal Natural Science Foundation (No. 11ZR1411500).