Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem

Summers, Sean; Lygeros, John

doi:10.1016/j.automatica.2010.08.006

Cited by 153 publications

(191 citation statements)

References 25 publications

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“…Equation (4) can be rewritten as in [7], [8] using indicator notation, with 1 A (x) = 1 for x ∈ A and 1 A (x) = 0 otherwise.…”

Section: B Reachabilitymentioning

confidence: 99%

“…In continuous time, level set methods can be used to approximate solutions to a stochastic HamiltonJacobi-Bellman equation, as in [5], [6]. In discrete time, dynamic programming has been used to solve such problems (and in particular for hybrid system dynamics, as in [7], [8]). In both cases, as the dimensionality of the system grows, the computational effort required for such problems renders a solution unattainable.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic reachability for control of spacecraft relative motion

Lesser

Oishi

Erwin

2013

52nd IEEE Conference on Decision and Control

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Abstract-The concept of stochastic reachability allows for the assessment, before any maneuvers are initiated, of the probability of successfully implementing a rendezvous or docking procedure for spacecraft. The so-called reach-avoid problem lets us find the probability of reaching a target set while avoiding some unsafe or undesired set, despite uncertainty due to nonlinearity and disturbances. This paper examines two novel methods for the calculation of stochastic reachable sets, and specifically for rendezvous and docking problems. In particular, we examine a) particle (or scenario) approximations to expected values, and b) conversion of the reach-avoid probability to a chance-constrained convex optimization problem. Both methods allow for computation of the reach-avoid set in higher dimensions, as compared to other existing methods for computing stochastic reachable sets. We describe in detail both of these methods, and then apply them to spacecraft relative motion, a four-dimensional problem.

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“…Equation (4) can be rewritten as in [7], [8] using indicator notation, with 1 A (x) = 1 for x ∈ A and 1 A (x) = 0 otherwise.…”

Section: B Reachabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic reachability for control of spacecraft relative motion

Lesser

Oishi

Erwin

2013

52nd IEEE Conference on Decision and Control

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“…in [APLS08, SL10,CCL11], however the results have either required restrictive conditions the on model or focused on special cases of the problem, for instance when only Markov (history-independent) policies are allowed. In contrast, here we consider the most general setting for the reachability problem, and we provide a complete treatment of the problem under conditions on the model being as mild as possible: this is considered to be the core of our contribution.…”

Section: Introductionmentioning

confidence: 99%

“…These results have been extended in [SL10], which has dealt with the general constrained reachability problem in the form of a sum-multiplicative cost…”

mentioning

confidence: 99%

“…To cope with this issue, extended Markov policies have been proposed in [KSL13], namely policies that can depend also on an additional historical variable -the state of the transition system, which is a deterministic function of the cdt-MP state history. 12 The constrained reachability problem is also known as the reach-avoid problem [SL10]. 13 As a side note, the constrained reachability can be also obtained from the unconstrained one by changing the dynamics of the cdt-MP on the set…”

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confidence: 99%

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Quantitative model-checking of controlled discrete-time Markov processes

Tkachev

Mereacre

Katoen

et al. 2017

Information and Computation

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ABSTRACT. This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of ω-regular properties can be reduced to the solution of one of two fundamental problems: reachability and repeated reachability. We provide a comprehensive study of the former problem and an initial characterisation of the (much more involved) latter problem. A case study elucidates concepts and techniques.

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Perception simplex: Verifiable collision avoidance in autonomous vehicles amidst obstacle detection faults

Bansal,

Kim,

et al. 2024

Software Testing Verif & Rel

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Advances in deep learning have revolutionized cyber‐physical applications, including the development of autonomous vehicles. However, real‐world collisions involving autonomous control of vehicles have raised significant safety concerns regarding the use of deep neural networks (DNNs) in safety‐critical tasks, particularly perception. The inherent unverifiability of DNNs poses a key challenge in ensuring their safe and reliable operation. In this work, we propose perception simplex (), a fault‐tolerant application architecture designed for obstacle detection and collision avoidance. We analyse an existing LiDAR‐based classical obstacle detection algorithm to establish strict bounds on its capabilities and limitations. Such analysis and verification have not been possible for deep learning‐based perception systems yet. By employing verifiable obstacle detection algorithms, identifies obstacle existence detection faults in the output of unverifiable DNN‐based object detectors. When faults with potential collision risks are detected, appropriate corrective actions are initiated. Through extensive analysis and software‐in‐the‐loop simulations, we demonstrate that provides deterministic fault tolerance against obstacle existence detection faults, establishing a robust safety guarantee.

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Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem

Cited by 153 publications

References 25 publications

Stochastic reachability for control of spacecraft relative motion

Stochastic reachability for control of spacecraft relative motion

Quantitative model-checking of controlled discrete-time Markov processes

Perception simplex: Verifiable collision avoidance in autonomous vehicles amidst obstacle detection faults

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