Rigorous Modeling of Hybrid Systems Using Interval Arithmetic Constraints

Hickey, Timothy J.; Wittenberg, David

doi:10.1007/978-3-540-24743-2_27

Cited by 18 publications

(12 citation statements)

References 24 publications

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“…For the purpose of taking into account more general differential equations. We are thinking to rather use an approach similar to the one proposed by Hickey [11].…”

Section: Discussionmentioning

confidence: 99%

Modeling the Molecular Network Controlling Adhesion Between Human Endothelial Cells: Inference and Simulation Using Constraint Logic Programming

Fanchon

Corblin

Trilling

et al. 2005

Computational Methods in Systems Biology

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Abstract. Cell-cell adhesion plays a critical role in the formation of tissues and organs. Adhesion between endothelial cells is also involved in the control of leukocyte migration across the endothelium of blood vessels. The most important players in this process are probably identified and the overall organization of the biochemical network can be drawn, but knowledge about connectivity is still incomplete, and the numerical values of kinetic parameters are unknown. This calls for qualitative modeling methods. Our aim in this paper is twofold: (i) to integrate in a unified model the biochemical network and the genetic circuitry. For this purpose we transform our system into a system of piecewise linear differential equations and then use Thomas theory of discrete networks.(ii) to show how constraints can be used to infer ranges of parameter values from observations and, with the same model, perform qualitative simulations.

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“…For the purpose of taking into account more general differential equations. We are thinking to rather use an approach similar to the one proposed by Hickey [11].…”

Section: Discussionmentioning

confidence: 99%

Modeling the Molecular Network Controlling Adhesion Between Human Endothelial Cells: Inference and Simulation Using Constraint Logic Programming

Fanchon

Corblin

Trilling

et al. 2005

Computational Methods in Systems Biology

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show abstract

“…Tightness of the interval enclosures, as expected for at least linear ODEs, can be demonstrated on a damped harmonic oscillator dx dt = y−0.8· x and dy dt = −x + 0.3 · y. While mere interval-based numeric overapproximation used in previous ICP-based approaches to reasoning about ODEs (e.g., [10]) does not accurately reflect the damping, yielding enclosures like the outer one in Fig. 3 (b), our approach yields a reasonably exact overapproximation of the pre-post-relation mediated by the ODE (Fig.…”

Section: First Experimental Resultsmentioning

confidence: 89%

“…This approach provides a technique for safely overapproximating the image under an ODE of a rectangular region in phase space and incorporates techniques based on coordinate transformations for mitigating the wrapping effect encountered upon iterating interval-based overapproximations of reachable state sets. (3) CLP(F) [10], offering a symbolic, constraint-based technology for reasoning about ODEs grounded in (in-)equational constraints obtained from Taylor expansions, thus being able to handle ODE parameters, error ranges in measurements, and other natural uncertainties in modeling dynamic systems. Such effects are hard to deal with, and hence often ignored, within numeric approaches to image computation.…”

Section: Introductionmentioning

confidence: 99%

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

Eggers

Fränzle

Herde

2008

Lecture Notes in Computer Science

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Abstract. In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving ordinary differential equations (ODEs), we provide a seamless integration of safe numeric overapproximation of initial-value problems into a SATmodulo-theory (SMT) approach to interval-based arithmetic constraint solving. Interval-based safe numeric approximation of ODEs is used as an interval contractor being able to narrow candidate sets in phase space in both temporal directions: post-images of ODEs (i.e., sets of states reachable from a set of initial values) are narrowed based on partial information about the initial values and, vice versa, pre-images are narrowed based on partial knowledge about post-sets. In contrast to the related CLP(F) approach of Hickey and Wittenberg [10], we do (a) support coordinate transformations mitigating the wrapping effect encountered upon iterating interval-based overapproximations of reachable state sets and (b) embed the approach into an SMT framework, thus accelerating the solving process through the algorithmic enhacements of recent SAT solving technology.

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“…use the Taylor-series-based enclosure method in the HyperTech tool [21], also facing hybrid systems analysis, however not in a constraint solving approach. In [23], CLP(F) -a very broad framework to constraint logic programming -is applied to models of hybrid systems. CLP(F) does however not include any measures against the wrapping effect encountered when enclosing ODE trajectories with intervals.…”

Section: Differential Equations As Constraintsmentioning

confidence: 99%

Challenges in Constraint-Based Analysis of Hybrid Systems

Eggers

Kalinnik

Kupferschmid

et al. 2009

Lecture Notes in Computer Science

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Abstract. In the analysis of hybrid discrete-continuous systems, rich arithmetic constraint formulae with complex Boolean structure arise naturally. The iSAT algorithm, a solver for such formulae, is aimed at bounded model checking of hybrid systems. In this paper, we identify challenges emerging from planned and ongoing work to enhance the iSAT algorithm: First, we propose an extension of iSAT to directly handle ordinary differential equations as constraints. Second, we outline the recently introduced generalization of the iSAT algorithm to deal with probabilistic hybrid systems and some open research issues in that context. Third, we present ideas on how to move from bounded to unbounded model checking by using the concept of interpolation. Finally, we discuss the adaption of some parallelization techniques to the iSAT case, which will hopefully lead to performance gains in the future. By presenting these open research questions, this paper aims at fostering discussions on these extensions of constraint solving.

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Rigorous Modeling of Hybrid Systems Using Interval Arithmetic Constraints

Cited by 18 publications

References 24 publications

Modeling the Molecular Network Controlling Adhesion Between Human Endothelial Cells: Inference and Simulation Using Constraint Logic Programming

Modeling the Molecular Network Controlling Adhesion Between Human Endothelial Cells: Inference and Simulation Using Constraint Logic Programming

SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems

Challenges in Constraint-Based Analysis of Hybrid Systems

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