The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Collins, Pieter; Goldsztejn, Alexandre

doi:10.1016/j.entcs.2008.12.033

Cited by 18 publications

(11 citation statements)

References 14 publications

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“…There Collins shows that, in general, the reachable set of some initial region can be semi-computed (technically, lowercomputed), but can only be computed under some special conditions. Another interesting algorithm to study the reachability problem is given in [15].…”

Section: Description Of Resultsmentioning

confidence: 99%

Computability and Dynamical Systems

Buescu

Graça

Zhong

2011

Dynamics, Games and Science I

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In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic.

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Section: Description Of Resultsmentioning

confidence: 99%

Computability and Dynamical Systems

Buescu

Graça

Zhong

2011

Dynamics, Games and Science I

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“…The goal of propagation techniques is to contract as much as possible the domains for the variables of a CN without loosing any solution. The principle is to decompose all constraints of the initial CN into primitive constraints and to call the corresponding contractors Chabert and Jaulin 2009;Collins and Goldsztejn 2008 until no more contraction can be observed. Therefore, constraint propagation is only able to find an outer approximation of the problem.…”

Section: Formalizationmentioning

confidence: 99%

Bracketing backward reach sets of a dynamical system

Mézo

Jaulin

Zerr

2019

International Journal of Control

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In this paper, we present a new method for bracketing (i.e., characterizing from inside and from outside) backward reach set of the target region T of a continuous time dynamical system. The principle of the method is to formalize the problem as a constraint network, where the variables are the trajectories (or paths) of the system. The resolution is made possible by using mazes which is a set of paths that contain all solutions of the problem. As a result, we will be able to derive a method able to compute a backward reach set for a huge class of systems without any knowledge of a parametric Lyapunov function and without assuming any linearity for our system. The method will be illustrated on several examples.

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“…Many previous studies have applied interval methods to reachability analysis of hybrid systems [8,5,24,15,3,11,12]. The outcome of these methods is an overapproximation of a set of reachable states with a set of boxes.…”

Section: Related Workmentioning

confidence: 99%

“…A fundamental process in formal methods for hybrid systems is computation of rigorously approximated reachable sets. The techniques based on interval analysis Ishii Yonezaki Goldsztejn (Section 3) have shown practicality in the reachability analysis of nonlinear and complex hybrid systems [8,5,24,15,3,11,12]. In these frameworks, computation is δcomplete [10]: function values are allowed to be perturbed within a predefined δ ∈ R >0 , and, by setting bounds in a problem description, many generically undecidable problems become decidable.…”

Section: Introductionmentioning

confidence: 99%

Monitoring Bounded LTL Properties Using Interval Analysis

Ishii

Yonezaki

Goldsztejn³

2015

Electronic Notes in Theoretical Computer Science

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Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We relax the problem to allow outputting an inconclusive result when verification process cannot succeed with a prescribed precision, and present an efficient and rigorous monitoring algorithm that demonstrates that the problem is decidable. This algorithm performs a forward simulation of a hybrid automaton, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. A continuous state at a certain time computed in each step is enclosed by an interval vector that is proven to contain a unique solution. In the experiments, we show that the proposed method provides a useful tool for formal analysis of nonlinear and complex hybrid systems.

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The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

Cited by 18 publications

References 14 publications

Computability and Dynamical Systems

Computability and Dynamical Systems

Bracketing backward reach sets of a dynamical system

Monitoring Bounded LTL Properties Using Interval Analysis

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