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Stochastic safety verification using barrier certificates
2004
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)
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We develop a new method for safety verification of stochastic systems based on functions of states termed barrier certificates. ...
Given a stochastic continuous or hybrid system and sets of initial and unsafe states, our method computes an upper bound on the probability that a trajectory of the system reaches the unsafe set, a bound ...
SAFETY VERIFICATION OF STOCHASTIC HYBRID SYSTEMS The idea used in Section III can also be applied to stochastic hybrid systems. ...
doi:10.1109/cdc.2004.1428804
fatcat:3s4j4zu4drflzkv5qtn7rjxn2m
Data-driven Safety Verification of Stochastic Systems via Barrier Certificates
[article]
2021
arXiv
pre-print
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We first reformulate the barrier-based safety verification as a robust convex problem (RCP). ...
The proposed framework is based on a notion of barrier certificates together with data collected from trajectories of unknown systems. ...
Safety verification
on Fundamentals of Electronics, Communications and of hybrid systems using barrier certificates. ...
arXiv:2112.12709v1
fatcat:fq5v6mh2hvhgrhtlwyfwqb7adu
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates
2007
IEEE Transactions on Automatic Control
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This paper presents a methodology for safety verification of continuous and hybrid systems in the worst-case and stochastic settings. ...
In the worst-case setting, a function of state termed barrier certificate is used to certify that all trajectories of the system starting from a given initial set do not enter an unsafe region. ...
In addition, by using barrier certificates that generate nonnegative supermartingales under the given system dynamics, we are able to handle safety verification of stochastic continuous and hybrid systems ...
doi:10.1109/tac.2007.902736
fatcat:idwocxaltbhrfjyfgm2hszykjm
Automated Verification and Synthesis of Stochastic Hybrid Systems: A Survey
[article]
2022
arXiv
pre-print
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stochastic similarity relations, (control) barrier certificates, compositional techniques, and a selection of results on continuous-time stochastic systems; we finally survey recently developed software ...
Automated verification and policy synthesis for stochastic hybrid systems can be inherently challenging: this is due to the heterogeneity of their dynamics (presence of continuous and discrete components ...
We hope that this survey article provides an introduction to the foundations of SHS, towards an easier understanding of many challenges and existing solutions related to formal verification and control ...
arXiv:2101.07491v2
fatcat:dpir554ebfclhpj5m7e7fi2hv4
Safety Barrier Certificates for Stochastic Hybrid Systems
[article]
2022
arXiv
pre-print
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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 and propose sufficient conditions to construct an ACBC based on CBC of original hybrid systems. ...
As a result, the existence of such a function provides a formal (probabilistic) certificate for the safety of the system. ...
arXiv:2208.03478v1
fatcat:2sheab2zrrc2fdd2t6l4vwmlp4
Unbounded-Time Safety Verification of Stochastic Differential Dynamics
[chapter]
2020
Lecture Notes in Computer Science
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This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time. ...
Previously the safety verification problem has been tackled over finite and infinite time horizons using a diverse set of approaches. ...
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]
2020
arXiv
pre-print
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This is achieved by discovering an exponential barrier certificate that proves exponentially converging bounds on the probability of safety violations over time. ...
Previously the safety verification problem has been tackled over finite and infinite time horizons using a diverse set of approaches. ...
Unbounded-time stochastic safety verification of SDE systems was first studied by Prajna et al. in [27, 28] , where a typical supermartingale was employed as a stochastic barrier certificate followed ...
arXiv:2006.01858v1
fatcat:rnht75insbdtvm52rvmoztmvqe
A Framework for Safe Probabilistic Invariance Verification of Stochastic Dynamical Systems
[article]
2024
arXiv
pre-print
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This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and continuous-time stochastic dynamical systems over an infinite time horizon. ...
These optimizations adapt classical stochastic barrier certificates, which are based on Doob's non-negative supermartingale inequality, and the equations described in [29],[31], which can precisely define ...
The first set of optimizations is adapted from stochastic barrier certificates for safety and reachability verification in [3] . ...
arXiv:2404.09007v1
fatcat:qopnauponjfjpkctmxd5qlu7si
Compositional Controller Synthesis for Interconnected Stochastic Systems with Markovian Switching
[article]
2022
arXiv
pre-print
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In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. ...
We then utilize dissipativity theory to compositionally construct barrier certificates for interconnected systems based on storage certificates of individual subsystems. ...
Stochastic safety verification using barrier certificates for switched diffusion processes and stochastic hybrid systems is, respectively, proposed in [18] and [19] . ...
arXiv:2208.03476v1
fatcat:mnim6gsasvcmjnlbtdgn4b6ymy
Data-driven verification and synthesis of stochastic systems via barrier certificates
[article]
2023
arXiv
pre-print
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2021 pre-print arXiv:2111.10330v1 fatcat:inyzusqlfjdylddbrptfybivf4
In this work, we study verification and synthesis problems for safety specifications over unknown discrete-time stochastic systems. ...
When a model of the system is available, barrier certificates have been successfully applied for ensuring the satisfaction of safety specifications. ...
In [19] , a framework is proposed for safety verification of stochastic systems using barrier certificates which is extended to stochastic hybrid systems. ...
arXiv:2111.10330v2
fatcat:4xja3l2djramlprj3kz3mibpz4
From Small-Gain Theory to Compositional Construction of Barrier Certificates for Large-Scale Stochastic Systems
[article]
2022
arXiv
pre-print
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This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against ...
barrier certificates of interconnected systems by employing some max-type small-gain conditions. ...
Controller synthesis for the finite-time safety of stochastic systems using control barrier certificates is discussed in [SDC19] . ...
arXiv:2101.06916v2
fatcat:siagoiua4rd6deb4kwyczwvqhi
Safety Certification for Stochastic Systems via Neural Barrier Functions
[article]
2022
arXiv
pre-print
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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. ...
The composition of a barrier function with a stochastic system forms a supermartingale, thus enabling the computation of the probability that the system stays in a safe set over a finite time horizon via ...
Conclusion We studied probabilistic safety certification of stochastic systems using Neural Barrier Function (NBF). ...
arXiv:2206.01463v1
fatcat:txs77wfx7zclpe5u4wklzvcjjm
Temporal Logic Verification of Stochastic Systems Using Barrier Certificates
[article]
2018
arXiv
pre-print
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This paper presents a methodology for temporal logic verification of discrete-time stochastic systems. ...
We propose to use barrier certificates for computations of such lower bounds, which is computationally much more efficient than the existing discretization-based approaches. ...
It is based on computation of barrier certificates and uses sum-of-squares optimization to find such bounds. ...
arXiv:1807.00064v1
fatcat:glohwzaiyjgujpt6x5rbwpqy3u
Compositional Synthesis of Control Barrier Certificates for Networks of Stochastic Systems against ω-Regular Specifications
[article]
2022
arXiv
pre-print
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This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. ...
The proposed framework leverages the interconnection topology and a notion of so-called control sub-barrier certificates of subsystems, which are used to compositionally construct control barrier certificates ...
We then leveraged the interconnection topology to construct control barrier certificates of the interconnected system using control sub-barrier certificates of subsystems by imposing some dissipativitytype ...
arXiv:2103.02226v2
fatcat:tcn7nxkejbcotam77rb6khm32q
Compositional Construction of Control Barrier Certificates for Large-Scale Stochastic Switched Systems
[article]
2020
arXiv
pre-print
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In this paper, we propose a compositional framework for the construction of control barrier certificates for large-scale stochastic switched systems accepting multiple control barrier certificates with ...
pseudo-barrier certificates of subsystems. ...
Stochastic safety verification using barrier certificates for switched diffusion processes and stochastic hybrid systems is, respectively, proposed in [WB17] and [HCL + 17] . ...
arXiv:2005.01287v1
fatcat:mylwwzcds5c4ncjsddrajlwin4
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