HySon: Set-based simulation of hybrid systems

Bouissou, Olivier; Mimram, Samuel; Chapoutot, Alexandre

doi:10.1109/rsp.2012.6380694

Cited by 24 publications

(14 citation statements)

References 10 publications

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“…The precision related to the bounded analysis is offset by the price of uncertainty: behaviours beyond the given time bound are not considered, and may thus violate a safety requirement. Representatives are STRONG [15], HySon [7] TABLE IV Comparison on convoyCar2 benchmark, between this work and the LGG algorithm [28] CORA [1], HYLAA [3] and SpaceEx [20].…”

Section: A Time-bounded Reachability Analysismentioning

confidence: 99%

Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration

et al. 2015

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Reachability analysis of continuous and discrete time systems is a hard problem that has seen much progress in the last decades. In many cases the problem has been reduced to bisimulations with a number of limitations in the nature of the dynamics, soundness, or time horizon. In this article we focus on sound safety verification of Unbounded-Time Linear Time-Invariant (LTI) systems with inputs using reachability analysis. We achieve this by using Abstract Acceleration, which over-approximates the reach tube of a system over unbounded time by using abstraction . The technique is applied to a number of models and the results show good performance when compared to state-of-the-art tools. I. IntroductionLinear loops are an ubiquitous programming pattern. Linear loops iterate over continuous variables, which are updated with a linear transformation. Linear loops may be guarded, i.e., terminate if a given linear condition holds. Inputs from the environment can be modelled by means of non-deterministic choices within the loop. These features make linear loops expressive enough to capture the dynamics of many hybrid dynamical models. The usage of such models in safety-critical embedded systems makes linear loops a fundamental target for formal methods.Many high-level requirements for embedded control systems can be modelled as safety properties, i.e. deciding reachability of certain bad states, in which the system exhibits unsafe behaviour. Bad states may, in linear loops, be encompassed by guard assertions.Reachability in linear programs, however, is a formidable challenge for automatic analysers: the problem is undecidable despite the restriction to linear transformations (i.e., linear dynamics) and linear guards.The goal of this article is to push the frontiers of unbounded-time reachability analysis: we aim at devising a method that is able to reason soundly about unbounded trajectories. We present a new approach for performing abstract acceleration. Abstract acceleration [26], [27], [34] approximates the effect of an arbitrary number of loop iterations (up to infinity) with a single, non-iterative transfer function that is applied to the entry state of the loop (i.e., to the set of initial conditions of the linear dynamics). This article extends the work in [34] to systems with non-deterministic inputs elaborating the details omitted in [39].The key contributions of this article are: 1) We present a new technique to include inputs (non-determinism) in the abstract acceleration of general linear loops. 2) We introduce the use of support functions in complex spaces, in order to increase the precision of previous abstract acceleration methods.

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Section: A Time-bounded Reachability Analysismentioning

confidence: 99%

Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration

et al. 2015

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“…Most of the recent work on the symbolic (or set-valued) integration of nonlinear ODEs is based on the upper bounding of the Lagrange remainders either in the framework of Taylor series or Runge-Kutta schemes [2,5,6,8,9,10,20,24,26]. Sets of states are generally represented as vectors of intervals (or "rectangles") and are manipulated through interval arithmetic [22] or affine arithmetic [27].…”

Section: Related Workmentioning

confidence: 99%

“…As said in [10], in the methods of symbolic analysis and control of hybrid systems, the way of representing sets of state values and computing reachable sets for systems defined by ordinary differential equations (ODEs) is fundamental (see, e.g., [2,14]). An interesting approach appeared recently, based on the propagation of reachable sets using guaranteed Runge-Kutta methods with adaptive step size control (see [6,17]). In [10] such guaranteed integration methods are used in the framework of sampled switched systems.…”

Section: Introductionmentioning

confidence: 99%

Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

Coënt

Vuyst

Chamoin

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed control. The benefit of this method is that the error introduced by symbolic modeling is bounded by choosing suitable time and space discretizations. The method is implemented in the interpreted language Octave. Several examples of the literature are performed and the results are compared with results obtained with a previous method based on the Runge-Kutta integration method.

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“…One can mention a first line of works in which zonotopes are used to precisely over-approximate set of values: 1. hybrid system simulation, for example recent Bouissou et al set-based simulation [BMC12] or earlier Girard work [Gir05]; 2. or floating point error propagation, eg. This characterizes the domains of boxes and zonotopes.…”

Section: Affine Arithmetics and Static Analysismentioning

confidence: 99%