Automated verification and synthesis of stochastic hybrid systems: A survey

Lavaei, Abolfazl; Soudjani, Sadegh; Abate, Alessandro

doi:10.1016/j.automatica.2022.110617

Cited by 67 publications

(33 citation statements)

References 160 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By contrast, most other abstraction methods (see the related work in Sect. 7 and the survey article Lavaei, Soudjani, Abate, & Zamani, 2022) rely on forward reachability computations, which are associated with errors that grow with the time horizon of the considered property. Our backward scheme avoids such abstraction errors, at the cost of requiring slightly more restrictive assumptions on the system dynamics.…”

Section: Distribution Of the Noisementioning

confidence: 99%

“…7 for more details. iMDPs have recently been proposed as an alternative to standard MDPs for abstracting stochastic dynamical systems (Cauchi, Laurenti, Lahijanian, Abate, Kwiatkowska, & Cardelli, 2019;Lavaei et al, 2022). We show explicitly how to lift the PAC guarantees on individual transition probabilities to a correctness guarantee on the whole iMDP.…”

Section: Distribution Of the Noisementioning

confidence: 99%

“…One notable feature of our abstraction scheme is that we can handle reach-avoid properties over infinite-time horizons, also known as unbounded properties (Tkachev & Abate, 2014). Most existing abstraction-based controller synthesis methods cause abstraction errors that grow with the time horizon and are thus limited to finite-horizon properties (Abate, Katoen, Lygeros, & Prandini, 2010;Soudjani & Abate, 2013;Lavaei et al, 2022;Zikelic, Lechner, Henzinger, & Chatterjee, 2022). By contrast, we provide a PAC guarantee on each transition probability interval of the iMDP being correct, without errors that grow with the horizon of the considered properties.…”

Section: Distribution Of the Noisementioning

confidence: 99%

See 2 more Smart Citations

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Badings¹,

Romao

Abate

et al. 2023

jair

View full text Add to dashboard Cite

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

show abstract

Section: Distribution Of the Noisementioning

confidence: 99%

Section: Distribution Of the Noisementioning

confidence: 99%

Section: Distribution Of the Noisementioning

confidence: 99%

See 1 more Smart Citation

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Badings¹,

Romao

Abate

et al. 2023

jair

View full text Add to dashboard Cite

show abstract

“…Model-based approaches. Abstractions of stochastic models are a well-studied research area (Abate et al 2008;Alur et al 2000), with applications to stochastic hybrid Lavaei et al 2021), 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).…”

Section: Related Workmentioning

confidence: 99%

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

Badings¹,

Romao²,

Abate³

et al. 2022

Preprint

View full text Add to dashboard Cite

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 and the presence of external disturbances lead 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 and disturbances are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based controller synthesis method for continuous-state models with stochastic noise, uncertain parameters, and external disturbances. 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 then synthesize an optimal policy on this abstract 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.

show abstract

“…This friendly competition is organized by Alessandro Abate (alessandro.abate@cs.ox.ac.uk), Stefan This report presents the results of the ARCH Friendly Competition 2022 in the group stochastic models. We refer the reader to the survey paper [53] and references therein for the details of most of the underlying techniques used in the development of the tools of this category. The following tools and frameworks have participated in this category so far: (in alphabetical order): AMYTISS, FAUST 2 , FIGARO workbench, hpnmg, HYPEG, Mascot-SDS, the Modest Toolset, ProbReach, PyCATSHOO, RealySt, SDCPN & IPS, SReachTools, StocHy, and SySCoRe.…”

Section: Introductionmentioning

confidence: 99%

ARCH-COMP22 Category Report: Stochastic Models

Abate¹,

Blom²,

Delicaris³

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

This report presents the results of a friendly competition for formal verification and policy synthesis of stochastic models. It also introduces new benchmarks and their properties within this category and recommends next steps for this category towards next year’s edition of the competition. In comparison with tools on non-probabilistic models, the tools for stochastic models are at the early stages of development that do not allow full competition on a standard set of benchmarks. We report on an initiative to collect a set of minimal benchmarks that all such tools can run, thus facilitating the comparison between efficiency of the implemented techniques. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in Summer 2022.

show abstract

Automated verification and synthesis of stochastic hybrid systems: A survey

Cited by 67 publications

References 160 publications

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

Robust Control for Dynamical Systems with Non-Gaussian Noise via Formal Abstractions

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

ARCH-COMP22 Category Report: Stochastic Models

Contact Info

Product

Resources

About