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

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• 作者：Qiuye Wang ; Yangjia Li ; Bican Xia ; Naijun Zhan
• 关键词：Hybrid systems ; invariants ; non ; autonomous systems ; polynomial ideals ; semi ; algebraic sets
• 刊名：Journal of Systems Science and Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：30
• 期：1
• 页码：234-252
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Operation Research/Decision Theory; Mathematics of Computing; Complex Systems; Statistics, general;
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences
• ISSN：1559-7067
• 卷排序：30

文摘

Hybrid systems are dynamical 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 the previous work, the fourth author and his coauthors 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. This paper considers how to extend their 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, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.