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Non-linear Continuous Systems for Safety Verification

Andrew Sogokon, Khalil Ghorbal, Taylor T Johnson
unpublished
We present a set of 65 safety verification problems featuring non-linear polynomial ODEs and for which we have proofs of safety.  ...  Safety verification of hybrid dynamical systems relies crucially on the ability to reason about reachable sets of continuous systems whose evolution is governed by a system of ordinary differential equations  ...  Acknowledgements The authors would very much like to thank the anonymous reviewers for their careful reading, pertinent points of critique and valuable suggestions for improving this document.  ... 
doi:10.29007/w94n fatcat:6zt2suaflnckvjiw6ftdjqcxgu

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  
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  ...  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.  ...  safety verification for hybrid dynamical systems.  ... 
doi:10.1007/978-3-662-49122-5_13 fatcat:wed2znuprjb6fb2boyynodfbg4

The d/dt Tool for Verification of Hybrid Systems [chapter]

Eugene Asarin, Thao Dang, Oded Maler
2002 Lecture Notes in Computer Science  
In this paper we describe the tool d/dt which provides automatic safety verification of hybrid systems with linear continuous dynamics with uncertain input.  ...  The tool also allows to synthesize a controller which switches the system between continuous modes in order to satisfy a safety specification.  ...  Conclusion and Related Work We have presented the tool d/dt for safety verification and switching controller synthesis for hybrid systems with linear differential inclusions.  ... 
doi:10.1007/3-540-45657-0_30 fatcat:alorpkppe5eihoo75xta2aqala

Linear invariant generation for verification of nonlinear hybrid systems via conservative approximation

Xia Zeng, Wang Lin, Zhengfeng Yang, Zhenbing Zeng
2016 Science China Information Sciences  
In this letter, we suggest a new method for safety verification of general nonlinear hybrid systems.  ...  In recent years, several methods, based on numeric computation and symbolic computation, have been proposed to compute invariants for safety verification of hybrid systems.  ...  Suppose that ϕ ℓ (x) 0, ℓ ∈ L are the computed linear invariants for safety verification of the uncertain linear hybrid system H u .  ... 
doi:10.1007/s11432-015-0980-7 fatcat:5n7fovwyi5fxtjobjvs4sl73ie

Formal Verification of Full-Wave Rectifier: A Case Study [article]

Kusum Lata, H S Jamadagni
2009 arXiv   pre-print
We have used the Checkmate tool from CMU [1], which is a public domain formal verification tool for hybrid systems.  ...  Due to the restriction imposed by Checkmate it necessitates to make the changes in the Checkmate implementation to implement the complex and non-linear system.  ...  non-linear differential-algebraic equations.  ... 
arXiv:0909.5393v1 fatcat:qy5iawuxfbbhrkbceqyhv24dhq

Verifying Safety and Persistence Properties of Hybrid Systems Using Flowpipes and Continuous Invariants [chapter]

Andrew Sogokon, Paul B. Jackson, Taylor T. Johnson
2017 Lecture Notes in Computer Science  
We propose a method for verifying persistence of nonlinear hybrid systems.  ...  The case study also nicely shows the richness of systems that the method can handle: the case study features a mode with non-polynomial (nonlinear) ODEs and we manage to prove the persistence property  ...  Acknowledgements The authors wish to thank the anonymous reviewers for their careful reading and valuable suggestions for improving this paper.  ... 
doi:10.1007/978-3-319-57288-8_14 fatcat:czwmyzclabgspnmq2pcdipdhfi

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.  ...  Vector Lyapunov functions are a multi-dimensional extension of the more familiar (scalar) Lyapunov functions, commonly used to prove stability properties in systems of non-linear ordinary differential  ...  for their detailed comments and scrutiny.  ... 
doi:10.1007/978-3-319-95582-7_25 fatcat:hrgch7sazvfmdcn2fhjrcbygna

Safety Verification of a Cooperative Vehicle Platoon with Uncertain Inputs Using Zonotopes*

Ibtissem Ben Makhlouf, Jan P. Maschuw, Paul Hänsch, Hilal Diab, Stefan Kowalewski, Dirk Abel
2011 IFAC Proceedings Volumes  
Our approach is based on the reachability analysis of linear systems subject to uncertain inputs. The reachable sets are represented by zonotopes.  ...  This paper presents an approach to safety verification of a controlled cooperative platoon of vehicles. To guarantee collision free operation, spacing errors must not exceed critical bounds.  ...  To verify safety, a verification method based on the reachability analysis of continuous linear systems with uncertain inputs is proposed.  ... 
doi:10.3182/20110828-6-it-1002.02165 fatcat:dizqliyzjrfb7j6fih6h25e77a

PTIME Parametric Verification of Safety Properties for Reasonable Linear Hybrid Automata

Werner Damm, Carsten Ihlemann, Viorica Sofronie-Stokkermans
2011 Mathematics in Computer Science  
This paper identifies an industrially relevant class of linear hybrid automata (LHA) called reasonable LHA for which parametric verification of convex safety properties with exhaustive entry states can  ...  be verified in polynomial time and time-bounded reachability can be decided in nondeterministic polynomial time for non-parametric verification and in exponential time for parametric verification.  ...  This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center "Automatic Verification and Analysis of Complex Systems" (SFB/TR 14 AVACS)  ... 
doi:10.1007/s11786-011-0098-x fatcat:sclmgq3pzvhzpaa42sulo35hqi

Formal verification of hybrid systems

Rajeev Alur
2011 Proceedings of the ninth ACM international conference on Embedded software - EMSOFT '11  
models for continuously evolving physical activities.  ...  In this article, we briefly review selected existing approaches to formal verification of hybrid systems, along with directions for future research.  ...  We thank Oded Maler and André Platzer for their feedback on this article.  ... 
doi:10.1145/2038642.2038685 dblp:conf/emsoft/Alur11 fatcat:wtxbmn6karefzhpzsuhugqnzsq

Scalable Synthesis of Verified Controllers in Deep Reinforcement Learning [article]

Zikang Xiong, Suresh Jagannathan
2021 arXiv   pre-print
There has been significant recent interest in devising verification techniques for learning-enabled controllers (LECs) that manage safety-critical systems.  ...  Our key insight involves separating safety verification from neural controller, using pre-computed verified safety shields to constrain neural controller training which does not only focus on safety.  ...  Stochastic Linear Time-Variant Transition System We also study our verification algorithm on the stochastic linear time-variant transition system.  ... 
arXiv:2104.10219v2 fatcat:wmghro6mpzcmboj2ai5ihlplju

Learning a Safety Verifiable Adaptive Cruise Controller from Human Driving Data [article]

Qin Lin, Sicco Verwer, John Dolan
2019 arXiv   pre-print
For safety-critical systems such as autonomous vehicles, it can be problematic to use controllers learned from data because they cannot be guaranteed to be collision-free.  ...  Besides being accurate, the logical nature of this model makes it suitable for formal verification. In this paper, we demonstrate this capability using the SpaceEx hybrid model checker as follows.  ...  SpaceEx SpaceEx is a powerful and popular tool for safety verification of hybrid systems.  ... 
arXiv:1910.13526v1 fatcat:vyxkylpr2jfxnlhpc4jlthszpa

Primal–Dual Tests for Safety and Reachability [chapter]

Stephen Prajna, Anders Rantzer
2005 Lecture Notes in Computer Science  
A methodology for safety verification using barrier certificates has been proposed recently.  ...  Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting  ...  The need for safety verification arises as the complexity of the system increases, and is also underscored by the safety critical nature of the system.  ... 
doi:10.1007/978-3-540-31954-2_35 fatcat:amhw32nrcnatpfv7ufagv2lqoe

NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems [chapter]

Hoang-Dung Tran, Xiaodong Yang, Diego Manzanas Lopez, Patrick Musau, Luan Viet Nguyen, Weiming Xiang, Stanley Bak, Taylor T. Johnson
2020 Lecture Notes in Computer Science  
This paper presents the Neural Network Verification (NNV) software tool, a set-based verification framework for deep neural networks (DNNs) and learning-enabled cyber-physical systems (CPS).  ...  For learning-enabled CPS, such as closed-loop control systems incorporating neural networks, NNV provides exact and over-approximate reachability analysis schemes for linear plant models and FFNN controllers  ...  Star Set [38, 41] (code) The star set is an efficient set representation for simulation-based verification of large linear systems [6, 7, 42] where the superposition property of a linear system can be  ... 
doi:10.1007/978-3-030-53288-8_1 fatcat:7ls6jm5w4rh2veqfzlytl3eciq

Verification of a primary-to-secondary leaking safety procedure in a nuclear power plant using coloured Petri nets

E. Németh, T. Bartha, Cs. Fazekas, K.M. Hangos
2009 Reliability Engineering & System Safety  
The composed plant and PRISE safety procedure system has also been analysed by simulation using CPN analysis tools.  ...  Because of the discrete nature of the verification, a Coloured Petri Net (CPN) representation is proposed for both the procedure and the plant model.  ...  This calls for applying the methodology of discrete-continuous hybrid systems [16] .  ... 
doi:10.1016/j.ress.2008.10.012 fatcat:yqfvefgo6nczdamecw277sg5a4
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