Safety Certification for Stochastic Systems via Neural Barrier Functions

Mathiesen, Frederik Baymler; Calvert, Simeon C.; Laurenti, Luca

doi:10.1109/lcsys.2022.3229865

Cited by 14 publications

(2 citation statements)

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“…discrete-time sensing and actuation. Alternatively, discretetime methods have shown success while also capturing the sampled-data complexities of most real-world systems [9], [10], [11], [12]. In this work we focus on extending the theory discrete-time stochastic safety involving discrete-time control barrier functions (DTCBFs) and c-martingales.…”

Section: Introductionmentioning

confidence: 99%

“…The stochastic DTCBF literature can, in general, be divided into two categories: firstly, risk-based constraints which can be extended to trajectory-long guarantees using the union bound [13], [14], [15] and secondly, martingale-based techniques which develop trajectory-long safety guarantees [6], [16], [12], [9] in a similar fashion to c-martingales [11]. Both the first and second class of methods have been demonstrated on real-world robotic systems ( [17] and [18], respectively).…”

Section: Introductionmentioning

confidence: 99%

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End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions

Cosner

Yue

Ames

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the worst-case disturbance will occur. In contrast, this paper utilizes Freedman's inequality in the context of discrete-time control barrier functions (DTCBFs) and c-martingales to provide stronger (less conservative) safety guarantees for stochastic systems. Our approach accounts for the underlying disturbance distribution instead of relying exclusively on its worst-case bound and does not require the barrier function to be upper-bounded, which makes the resulting safety probability bounds more directly useful for intuitive safety constraints such as signed distance. We compare our results with existing safety guarantees, such as input-to-state safety (ISSf) and martingale results that rely on Ville's inequality. When the assumptions for all methods hold, we provide a range of parameters for which our guarantee is stronger. Finally, we present simulation examples, including a bipedal walking robot, that demonstrate the utility and tightness of our safety guarantee.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions

Cosner

Yue

Ames

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systems

Zhi,

Wang,

Liu

et al. 2024

Lecture Notes in Computer Science

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The rapid advance of deep reinforcement learning techniques enables the oversight of safety-critical systems through the utilization of Deep Neural Networks (DNNs). This underscores the pressing need to promptly establish certified safety guarantees for such DNN-controlled systems. Most of the existing verification approaches rely on qualitative approaches, predominantly employing reachability analysis. However, qualitative verification proves inadequate for DNN-controlled systems as their behaviors exhibit stochastic tendencies when operating in open and adversarial environments. In this paper, we propose a novel framework for unifying both qualitative and quantitative safety verification problems of DNN-controlled systems. This is achieved by formulating the verification tasks as the synthesis of valid neural barrier certificates (NBCs). Initially, the framework seeks to establish almost-sure safety guarantees through qualitative verification. In cases where qualitative verification fails, our quantitative verification method is invoked, yielding precise lower and upper bounds on probabilistic safety across both infinite and finite time horizons. To facilitate the synthesis of NBCs, we introduce their k-inductive variants. We also devise a simulation-guided approach for training NBCs, aiming to achieve tightness in computing precise certified lower and upper bounds. We prototype our approach into a tool called and showcase its efficacy on four classic DNN-controlled systems.

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