ProbReach: A Tool for Guaranteed Reachability Analysis of Stochastic Hybrid Systems

Shmarov, Fedor; Zuliani, Paolo

doi:10.29007/mh2c

Cited by 8 publications

(6 citation statements)

References 20 publications

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“…Abstractions of stochastic models are well-studied (Abate et al 2008;Alur et al 2000), with applications to stochastic hybrid Lavaei et al 2022), switched (Lahijanian, Andersson, and Belta 2015), and partially observable systems (Badings et al 2021;Haesaert et al 2018). Various tools exist, e.g., StocHy , ProbReach (Shmarov and Zuliani 2015), and SReachTools (Vinod, Gleason, and Oishi 2019). However, these papers only reason over uncertainty in a probabilistic way but do not ensure robustness as we do.…”

Section: Related Workmentioning

confidence: 99%

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Badings

Romao

Abate

et al. 2023

AAAI

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Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise and uncertain parameters. By sampling techniques and robust analysis, we capture both aleatoric and epistemic uncertainty, with a user-specified confidence level, in the transition probability intervals of a so-called interval Markov decision process (iMDP). We synthesize an optimal policy on this iMDP, which translates (with the specified confidence level) to a feedback controller for the continuous model with the same performance guarantees. Our experimental benchmarks confirm that accounting for epistemic uncertainty leads to controllers that are more robust against variations in parameter values.

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Section: Related Workmentioning

confidence: 99%

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Badings

Romao

Abate

et al. 2023

AAAI

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“…Other Formalisms. Several existing formalisms for stochastic hybrid models do not fit into the proposed classification, as they focus e.g., solely on randomly distributed initial states [18] or on a non-deterministic choice over discrete probability distributions for choosing a successor state [21].…”

Section: Classification Of Existing Approachesmentioning

confidence: 99%

Comparing Two Approaches to Include Stochasticity in Hybrid Automata

Willemsen,

Remke,

Ábrahám

2023

Lecture Notes in Computer Science

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Different stochastic extensions of hybrid automata have been proposed in the past, with unclear expressivity relations between them. To structure and relate these modeling languages, in this paper we formalize two alternative approaches to extend hybrid automata with stochastic choices of discrete events and their time points. The first approach, which we call decomposed scheduling, adds stochasticity via stochastic races, choosing random time points for the possible discrete events and executing a winner with an earliest time. In contrast, composed scheduling first samples the time point of the next event and then the event to be executed at the sampled time point. We relate the two approaches regarding their expressivity and categorize available stochastic extensions of hybrid automata from the literature.

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“…Whenever the initial set B 0 is known from the context, we simply refer to the reachset as the Reachset at time t j , or B j . (Kapela et al 2020) yes no Lohner algorithm yes Flow-star (Chen et al 2013) yes no Taylor models yes δ-reachability (Gao et al 2013) yes no approximate satisfiability yes C2E2 (Duggirala et al 2015) yes no discrepancy function yes LDFM (Fan et al 2017) yes yes simulation, matrix measures no TIRA (Meyer et al 2019) yes yes second-order sensitivity no Isabelle/HOL (Immler 2015) yes no proof-assistant yes Breach (Donzé et al 2007) yes yes simulation, sensitivity no PIRK (Devonport et al 2020) yes yes simulation, contraction bounds no HR (Li et al 2020) yes no hybridization yes ProbReach (Shmarov et al 2015a) no no δ-reachability, probability interval yes VSPODE (Enszer et al 2011) no no p-boxes yes GP (Bortolussi et al 2014) no no Gaussian process no SLR Ours no yes stochastic Lagrangian reachability no…”

Section: Setupmentioning

confidence: 99%

On the Verification of Neural ODEs with Stochastic Guarantees

Gruenbacher

Hasani

Lechner

et al. 2021

AAAI

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We show that Neural ODEs, an emerging class of time-continuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Stochastic Lagrangian Reachability (SLR), an abstraction-based technique for constructing a tight Reachtube (an over-approximation of the set of reachable states over a given time-horizon), and provide stochastic guarantees in the form of confidence intervals for the Reachtube bounds. SLR inherently avoids the infamous wrapping effect (accumulation of over-approximation errors) by performing local optimization steps to expand safe regions instead of repeatedly forward-propagating them as is done by deterministic reachability methods. To enable fast local optimizations, we introduce a novel forward-mode adjoint sensitivity method to compute gradients without the need for backpropagation. Finally, we establish asymptotic and non-asymptotic convergence rates for SLR.

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ProbReach: A Tool for Guaranteed Reachability Analysis of Stochastic Hybrid Systems

Cited by 8 publications

References 20 publications

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic Dynamical Models with Epistemic Uncertainty

Comparing Two Approaches to Include Stochasticity in Hybrid Automata

On the Verification of Neural ODEs with Stochastic Guarantees

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