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, m...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.展开更多
The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained...The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained.Furthermore,the relationship between stability radius and thesolvability of some type of algebraic Riccati equations is given.展开更多
基金supported partly by“973 Program”under Grant No.2014CB340701by the National Natural Science Foundation of China under Grant Nos.61625205,91418204 and 61625206+2 种基金by CDZ Project CAP(GZ 1023)by the CAS/SAFEA International Partnership Program for Creative Research Teamssupported partly by the National Natural Science Foundation of China under Grant Nos.11290141,11271034 and 61532019
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.
基金supported by the National Natural Science Foundation of China under Grant Nos. 10626057 and 10571165
文摘The authors discuss the stability radius of the non-smooth Pritchard-Salamon systemsunder structured perturbations.A formula for the stability radius in terms of t he norm of a certaininput-output operator is obtained.Furthermore,the relationship between stability radius and thesolvability of some type of algebraic Riccati equations is given.
