Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamic systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In our previous work, we gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. In this paper, we consider how to extend our previous work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, we present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based WANG Qiuye, Yangjia Li and Naijun Zhan State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China E-mail : {wangqye,yangjia,znj}@ios.ac.cn XIA Bican LMAM & School of Math. Sci., Peking University, Beijing, China E-mail : [email protected] ∗ The first, second and fourth authors are supported partly by “973 Program” under grant No. 2014CB340701, by NSFC under grants 91418204 and 61625206, by CDZ project CAP (GZ 1023), and by the CAS/SAFEA International Partnership Program for Creative Research Teams; the third author is supported partly by NSFC under grants 11290141, 11271034 and 61532019. This paper was recommended for publication by Editor .... 2 WANG QIUYE · LI YANGJIA · XIA BICAN · ZHAN NAIJUN on which, we propose a sound and complete algorithm to generate all invariants with a pre-defined template.