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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
In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems.  ...  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 (called Exponential Condition) for the safety verification of semialgebraic hybrid systems.  ... 
arXiv:1303.6885v1 fatcat:ytgpqpg6pfe4lchcji3sgdpzhu

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  
In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems.  ...  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 (called Exponential Condition) for the safety verification of semialgebraic hybrid systems.  ... 
doi:10.1007/978-3-642-39799-8_17 fatcat:7zeuvrv5mbb5teg5ux6thtg2um

Safety Verification of Hybrid Automata with Transient Safe Modes

Guobin Wang, Jing Liu
2016 International Journal of Modeling and Optimization  
A new kind of barrier certificate with time constraints is proposed to derive a criterion for safety of such kind of hybrid automata.  ...  The validity of the proposed verification method is supported by a numerical example. Index Terms-Formal methods, hybrid system, safety verification.  ...  In this paper, we follow the basic idea of safety verification based on sum-of-squares (SOS) programming [8] , [9] and adopt an exponential-conditioned barrier certificate [10] , [11] to estimate  ... 
doi:10.7763/ijmo.2016.v6.533 fatcat:342iqkmor5cijhho6k55ep2sxm

Unbounded-Time Safety Verification of Stochastic Differential Dynamics [chapter]

Shenghua Feng, Mingshuai Chen, Bai Xue, Sriram Sankaranarayanan, Naijun Zhan
2020 Lecture Notes in Computer Science  
This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time.  ...  In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon.  ...  Section 3 elucidates the reduction of unbounded safety verification to bounded ones based on the witness of stochastic barrier certificates.  ... 
doi:10.1007/978-3-030-53291-8_18 fatcat:shz67g5jpfbq7jf4zhiqwwl5em

Unbounded-Time Safety Verification of Stochastic Differential Dynamics [article]

Shenghua Feng, Mingshuai Chen, Bai Xue, Sriram Sankaranarayanan, Naijun Zhan
2020 arXiv   pre-print
This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time.  ...  In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon.  ...  Sect. 3 elucidates the reduction of unbounded safety verification to bounded ones based on the witness of stochastic barrier certificates.  ... 
arXiv:2006.01858v1 fatcat:rnht75insbdtvm52rvmoztmvqe

Formal verification of hybrid systems

Rajeev Alur
2011 Proceedings of the ninth ACM international conference on Embedded software - EMSOFT '11  
In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.  ...  The appropriate mathematical model for embedded control systems is hybrid systems that combines the traditional state-machine based models for discrete control with classical differential-equations based  ...  We thank Oded Maler and André Platzer for their feedback on this article.  ... 
doi:10.1145/2038642.2038685 dblp:conf/emsoft/Alur11 fatcat:wtxbmn6karefzhpzsuhugqnzsq

A Novel Approach for Solving the BMI Problem in Barrier Certificates Generation [chapter]

Xin Chen, Chao Peng, Wang Lin, Zhengfeng Yang, Yifang Zhang, Xuandong Li
2020 Lecture Notes in Computer Science  
Barrier certificates generation is widely used in verifying safety properties of hybrid systems because of the relatively low computational complexity it costs.  ...  In addition, different from popular LMI solving based methods, it does not make the verification conditions more conservative, and thus reduces the risk of missing feasible solutions.  ...  [16] proposed an exponential condition for semi-algebraic hybrid systems. Kapinski et al. [12] diagnosed convex verification conditions to Lyapunov-based barrier certificates. C. Sloth et al.  ... 
doi:10.1007/978-3-030-53288-8_29 fatcat:h5wnfdnkazfobfs32ybek5phlu

Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models [article]

Andrea Peruffo, Daniele Ahmed, Alessandro Abate
2020 arXiv   pre-print
We introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models.  ...  , with in particular a stark speedup on the verification engine (up to five orders less), whilst needing a far smaller data set (up to three orders less) for the learning part.  ...  Introduction Barrier Certificates (BC) are an effective and powerful technique to prove safety properties on models of continuous and hybrid dynamical systems [20, 21] .  ... 
arXiv:2007.03251v2 fatcat:voq7prf6fzhslodibxnt3httqq

Automated and Formal Synthesis of Neural Barrier Certificates for Dynamical Models [chapter]

Andrea Peruffo, Daniele Ahmed, Alessandro Abate
2021 Lecture Notes in Computer Science  
AbstractWe introduce an automated, formal, counterexample-based approach to synthesise Barrier Certificates (BC) for the safety verification of continuous and hybrid dynamical models.  ...  , with in particular a stark speedup on the verification engine (up to three orders less), whilst needing a far smaller data set (up to three orders less) for the learning part.  ...  enriched counter-example generation, prioritised check of the verification constraints, and c) we newly synthesise verified barrier certificates for hybrid models, which are generated using counterexample-based  ... 
doi:10.1007/978-3-030-72016-2_20 fatcat:bpbllc6omzedhowy3gvwextkjq

Vector Barrier Certificates and Comparison Systems [chapter]

Andrew Sogokon, Khalil Ghorbal, Yong Kiam Tan, André Platzer
2018 Lecture Notes in Computer Science  
This paper explores an analogous vector extension for so-called barrier certificates used in safety verification.  ...  of vector barrier certificates in safety verification and invariant synthesis.  ...  for their detailed comments and scrutiny.  ... 
doi:10.1007/978-3-319-95582-7_25 fatcat:hrgch7sazvfmdcn2fhjrcbygna

Verifying Hybrid Systems Involving Transcendental Functions [chapter]

Paul Jackson, Andrew Sogokon, James Bridge, Lawrence Paulson
2014 Lecture Notes in Computer Science  
We explore uses of a link we have constructed between the KeYmaera hybrid systems theorem prover and the MetiTarski proof engine for problems involving special functions such as sin, cos, exp, etc.  ...  Transcendental functions arise in the specification of hybrid systems and often occur in the solutions of the differential equations that govern how the states of hybrid systems evolve over time.  ...  We extend special thanks to Grant Passmore at the LFCS, University of Edinburgh, for offering his expert advice.  ... 
doi:10.1007/978-3-319-06200-6_14 fatcat:wh7b6gdidbcfjkm7l2dos5tu4q

Safety Barrier Certificates for Stochastic Hybrid Systems [article]

Abolfazl Lavaei, Sadegh Soudjani, Emilio Frazzoli
2022 arXiv   pre-print
We then introduce an augmented control barrier certificate (ACBC) for augmented systems and propose sufficient conditions to construct an ACBC based on CBC of original hybrid systems.  ...  Our proposed framework leverages the notion of control barrier certificates (CBC), as a discretization-free approach, to synthesize safety controllers for stochastic hybrid systems while providing safety  ...  We then introduce an augmented control barrier certificate (ACBC) for augmented systems by proposing required conditions for the construction of ACBC based on CBC of original hybrid systems.  ... 
arXiv:2208.03478v1 fatcat:2sheab2zrrc2fdd2t6l4vwmlp4

Secure-by-Construction Synthesis of Cyber-Physical Systems [article]

Siyuan Liu, Ashutosh Trivedi, Xiang Yin, Majid Zamani
2022 arXiv   pre-print
We posit that, to truly realize the dream of correct-by-construction synthesis for security-critical systems, security considerations must take center-stage with the safety considerations.  ...  Correct-by-construction synthesis is a cornerstone of the confluence of formal methods and control theory towards designing safety-critical systems.  ...  For the barrier-based approach, appropriate conditions for barrier certificates of α-opacity also need to be identified. Quantitative Verification of Opacity.  ... 
arXiv:2202.06677v1 fatcat:366ep562mjc3xf5muj3evfzgtm

Safety Certification for Stochastic Systems via Neural Barrier Functions [article]

Frederik Baymler Mathiesen, Simeon Calvert, Luca Laurenti
2022 arXiv   pre-print
Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications.  ...  However, existing approaches to find barrier functions for stochastic systems generally rely on convex optimization programs that restrict the search of a barrier to a small class of functions such as  ...  Related works Safety certification of dynamical systems Safety guarantees for dynamical systems can be generally obtained with two different approaches: abstraction-based methods where the system is abstracted  ... 
arXiv:2206.01463v1 fatcat:txs77wfx7zclpe5u4wklzvcjjm

Hybrid Controller for Wind Turbine Generators to Ensure Adequate Frequency Response in Power Networks

Yichen Zhang, Kevin Tomsovic, Seddik M. Djouadi, Hector Pulgar-Painemal
2017 IEEE Journal on Emerging and Selected Topics in Circuits and Systems  
Due to increasing penetration, the hybrid behavior of CIPS, such as, wind turbine generators (WTG), may have significant impact on power system dynamics.  ...  The barrier certificate methodology is employed to derive a new algorithm to obtain and enlarge the ROS for the given desired safe limits and the worst-case disturbance scenarios.  ...  for hybrid system safety verification [11] .  ... 
doi:10.1109/jetcas.2017.2675879 fatcat:ckonlcrvizelhfxuohjp4md2tm
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