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A Method for Invariant Generation for Polynomial Continuous Systems [chapter]

Andrew Sogokon, Khalil Ghorbal, Paul B. Jackson, André Platzer
2015 Lecture Notes in Computer Science  
This paper presents a method for generating semi-algebraic invariants for systems governed by non-linear polynomial ordinary differential equations under semi-algebraic evolution constraints.  ...  Based on the notion of discrete abstraction, our method eliminates unsoundness and unnecessary coarseness found in existing approaches for computing abstractions for non-linear continuous systems and is  ...  Discrete abstraction of continuous systems was previously studied in [2, 3] (for linear systems) and [36, 37] (for more general non-linear systems), where a simple method for constructing abstractions  ... 
doi:10.1007/978-3-662-49122-5_13 fatcat:wed2znuprjb6fb2boyynodfbg4

Pegasus: Sound Continuous Invariant Generation [article]

Andrew Sogokon, Stefan Mitsch, Yong Kiam Tan, Katherine Cordwell, André Platzer
2020 arXiv   pre-print
There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different  ...  Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems.  ...  Acknowledgements The authors would like to thank the anonymous reviewers for providing valuable feedback and FM 2019 for the special issue invitation.  ... 
arXiv:2005.09348v2 fatcat:4bwfemvuu5g7ln25bcnn74yslq

Pegasus: sound continuous invariant generation

Andrew Sogokon, Stefan Mitsch, Yong Kiam Tan, Katherine Cordwell, André Platzer
2021 Formal methods in system design  
There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different  ...  Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems.  ...  Acknowledgements The authors would like to thank the guest editor for handling this article, the anonymous reviewers for providing value feedback, and FM 2019 for the special issue invitation.  ... 
doi:10.1007/s10703-020-00355-z fatcat:6bzcbvszcfbedifbtuezu6xzuq

Generating invariants of hybrid systems via sums-of-squares of polynomials with rational coefficients

Min Wu, Zhengfeng Yang
2011 Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11  
In this paper we discuss how to generate inequality invariants for continuous dynamical systems involved in hybrid systems.  ...  A hybrid symbolic-numeric algorithm is presented to compute inequality invariants of the given systems, by transforming this problem into a parameterized polynomial optimization problem.  ...  Acknowledgments We wish to thank Professor Lu Yang for his valuable suggestions on improving our two examples, and we also thank the reviewers for their helpful comments.  ... 
doi:10.1145/2331684.2331701 dblp:conf/snc/WuY11 fatcat:766qpvcmoreuva5rmvdwp4fr6u

Computing semi-algebraic invariants for polynomial dynamical systems

Jiang Liu, Naijun Zhan, Hengjun Zhao
2011 Proceedings of the ninth ACM international conference on Embedded software - EMSOFT '11  
In this paper, we consider an extended concept of invariant for polynomial dynamical systems (PDSs) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic  ...  A direct consequence of this criterion is a relatively complete method of SAI generation based on template assumption and semi-algebraic constraint solving.  ...  Xia Bican for their insightful comments on the earlier drafts. We thank Dr. Xu Ming, Zou Liang and Quan Zhao for helpful discussions and technical support.  ... 
doi:10.1145/2038642.2038659 dblp:conf/emsoft/LiuZZ11 fatcat:isfag6pkubfixhswsp3cta547a

Computing Semi-algebraic Invariants for Polynomial Dynamical Systems [article]

Jiang Liu and Naijun Zhan and Hengjun Zhao
2011 arXiv   pre-print
In this paper, we consider an extended concept of invariant for polynomial dynamical system (PDS) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic  ...  A direct consequence of this criterion is a relatively complete method of SAI generation based on template assumption and semi-algebraic constraint solving.  ...  CASE STUDY In this section, we show that our method presented above can be used to generate continuous invariants for some real systems.  ... 
arXiv:1102.0705v2 fatcat:kqhsupeanngtfjaiyno5a6khgy

Safety verification of semi-algebraic dynamical systems via inductive invariant

Hui Kong, Fei He, Xiaoyu Song, Ming Gu, Hongyan Tan, Jiaguang Sun
2014 Tsinghua Science and Technology  
In this paper, to lay a solid foundation for future research into the safety verification of semialgebraic dynamical systems, we first establish a formal framework for evaluating the quality of continuous  ...  In addition, we propose a new complete and computable inductive condition for verifying the safety of semi-algebraic dynamical systems.  ...  It is difficult to compute a continuous inductive invariant for a general continuous dynamical system is very hard.  ... 
doi:10.1109/tst.2014.6787375 fatcat:nw47dh4nqrd43jol6h56glwbfu

Exponential-Condition-Based Barrier Certificate Generation for Safety Verification of Hybrid Systems [chapter]

Hui Kong, Fei He, Xiaoyu Song, William N. N. Hung, Ming Gu
2013 Lecture Notes in Computer Science  
A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system.  ...  In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems.  ...  Construction Method for Barrier Certificate Constructing inductive invariants for general hybrid systems is very hard.  ... 
doi:10.1007/978-3-642-39799-8_17 fatcat:7zeuvrv5mbb5teg5ux6thtg2um

Exponential-Condition-Based Barrier Certificate Generation for Safety Verification of Hybrid Systems [article]

Hui Kong, Fei He, Xiaoyu Song, William N. N. Hung, Ming Gu
2013 arXiv   pre-print
A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system.  ...  In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems.  ...  x 21 : r Guard x x o Construction Method for Barrier Certificate Constructing inductive invariants for general hybrid systems is very hard.  ... 
arXiv:1303.6885v1 fatcat:ytgpqpg6pfe4lchcji3sgdpzhu

Synthesizing Switching Controllers for Hybrid Systems by Generating Invariants [chapter]

Hengjun Zhao, Naijun Zhan, Deepak Kapur
2013 Lecture Notes in Computer Science  
This is achieved by combining a QE (quantifier elimination)-based method for generating invariants with a qualitative approach for predefining templates.  ...  We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials.  ...  Jiang Liu for his great contribution to our previous joint work on invariant generation. We also thank Dr. Matthias Horbach, Mr.  ... 
doi:10.1007/978-3-642-39698-4_22 fatcat:na6ge7pjandallod5rdqksmyd4

Safety Verification of Nonlinear Hybrid Systems Based on Invariant Clusters

Hui Kong, Sergiy Bogomolov, Christian Schilling, Yu Jiang, Thomas A. Henzinger
2017 Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control - HSCC '17  
Based on invariant clusters and sum-of-squares (SOS ) programming, we present a new method for the safety verification of hybrid systems.  ...  For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g( u, x), an invariant cluster can be obtained by first computing the  ...  Hybrid Systems).  ... 
doi:10.1145/3049797.3049814 dblp:conf/hybrid/KongBSJH17 fatcat:vzo3ecz555gkhe7deylhrelxuq

Constructing invariants for hybrid systems

Sriram Sankaranarayanan, Henny B. Sipma, Zohar Manna
2007 Formal methods in system design  
An invariant of a system is a predicate that holds for every reachable state. In this paper, we present techniques to generate invariants for hybrid systems.  ...  This is achieved by reducing the invariant generation problem to a constraint solving problem using methods from the theory of ideals over polynomial rings.  ...  In this paper, we provide techniques to generate invariants for hybrid systems. An invariant of a hybrid system is a property ψ that holds in all the reachable states of the system.  ... 
doi:10.1007/s10703-007-0046-1 fatcat:qcjbhu3z5bhpdeojln2vbmy3xy

Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares Representation [article]

Wang Lin and Min Wu and Zhengfeng Yang and Zhenbing Zeng
2011 arXiv   pre-print
In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems.  ...  A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares (SOS) relaxation.  ...  Recently, some methods [20, 21, 25, 28] based on invariant generation have been proposed for safety verification of hybrid systems.  ... 
arXiv:1112.2328v1 fatcat:k67jsvzllje57j6xz6esratasy

Synthesizing Switching Controllers for Hybrid Systems by Continuous Invariant Generation [article]

Deepak Kapur, Naijun Zhan, Hengjun Zhao
2013 arXiv   pre-print
This is achieved by combining a QE (quantifier elimination)-based method for generating continuous invariants with a qualitative approach for predefining templates.  ...  We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials.  ...  Jiang Liu for his contribution to our previous joint work on invariant generation. We also thank Dr. Matthias Horbach and Mr. ThanhVu Nguyen for their valuable comments on our old drafts.  ... 
arXiv:1304.0825v1 fatcat:ygwraqcmbvbwbdlekx2anqcfni

Constructing Invariants for Hybrid Systems [chapter]

Sriram Sankaranarayanan, Henny B. Sipma, Zohar Manna
2004 Lecture Notes in Computer Science  
An invariant of a system is a predicate that holds for every reachable state. In this paper, we present techniques to generate invariants for hybrid systems.  ...  This is achieved by reducing the invariant generation problem to a constraint solving problem using methods from the theory of ideals over polynomial rings.  ...  In this paper, we provide techniques to generate invariants for hybrid systems. An invariant of a hybrid system is a property ψ that holds in all the reachable states of the system.  ... 
doi:10.1007/978-3-540-24743-2_36 fatcat:smozzk3ztzfirnhm5str3pnz4q
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