Dynamic optimization of interval narrowing algorithms

Lhomme, Olivier; Gotlieb, Arnaud; Rueher, Michel

doi:10.1016/s0743-1066(98)10007-9

Cited by 35 publications

(19 citation statements)

References 21 publications

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“…To some extent, this situation has already been acknowledged by interval constraint researchers: in a more general settings, Lhomme et al [9] noticed that during the propagation of domain variations (i.e., primary iteration), many applications of narrowing operators (that is, secondary iterations in our parlance) are unnecessary. They suggest a scheme to identify these useless operators by looking for static and dynamic dependencies; they then allocate the bulk of the computing power to but a subset of all the operators.…”

Section: Choosing a Good Transversalmentioning

confidence: 95%

On considering an interval constraint solving algorithm as a free-steering nonlinear Gauss-Seidel procedure

Goualard¹

2005

Proceedings of the 2005 ACM Symposium on Applied Computing

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We show that a classical interval constraint propagation algorithm enforcing box consistency may be interpreted as a free-steering nonlinear Gauss-Seidel procedure. This suggests that the choice of a transversal in the incidence matrix associated with the problem to solve is paramount to the efficiency of the algorithm. We present experimental evidences that it is indeed so, and we suggest an heuristics to compute good transversals. The improved interval constraint algorithm is compared with a classical one and with standard methods such as Hansen-Sengupta on some well-known benchmarks.

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Section: Choosing a Good Transversalmentioning

confidence: 95%

On considering an interval constraint solving algorithm as a free-steering nonlinear Gauss-Seidel procedure

Goualard¹

2005

Proceedings of the 2005 ACM Symposium on Applied Computing

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“…In the presented work, we use the forward-backward algorithm. The principle is to decompose the constraint equation f ([x 1 ], ..., [x n ]) = 0 in a sequence of elementary operations of primitive functions like {+, −, * , /} and obtain a list of primitive constraints ( [22]). For example, consider the following equation:…”

Section: Over Estimation Control 1) Gain Value Propagation: the Inmentioning

confidence: 99%

Improvements in computational aspects of interval Kalman filtering enhanced by constraint propagation

Jun¹,

Jauberthie²,

Travé-Massuyès³

2013

2013 IEEE 11th International Workshop of Electronics, Control, Measurement, Signals and Their Application to Mechatronics

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This paper deals with computational aspects of interval kalman filtering of discrete time linear models with bounded uncertainties on parameters and gaussian measurement noise. In this work, we consider an extension of conventional Kalman filtering to interval linear models [1]. As the expressions for deriving the Kalman filter involve matrix inversion which is known to be a difficult problem. One must hence find a way to implement or avoid this tricky algebraic operation within an interval framework. To solve the interval matrix inversion problem and other problems due to interval calculus, we propose an original approach combining the set inversion algorithm SIVIA and constraint satisfaction propagation. Several contractors are proposed to limit overestimation effects propagating within the interval Kalman filter recursive structure. Thus the description of our approach is followed by an application and we compare the proposed approach with interval kalman filtering developped in [1].

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“…There are several variants, alternatives, and improvements of the basic approach described above [Jaulin et al 2001;Benhamou et al 1994;Lhomme 1993;Lhomme et al 1998;Hickey 2001;Lebbah et al 2002].…”

Section: Constraint Solvingmentioning

confidence: 99%

Safety verification of hybrid systems by constraint propagation-based abstraction refinement

Ratschan

She

2007

ACM Trans. Embed. Comput. Syst.

175

103

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This paper deals with the problem of safety verification of nonlinear hybrid systems. We start from a classical method that uses interval arithmetic to check whether trajectories can move over the boundaries in a rectangular grid. We put this method into an abstraction refinement framework and improve it by developing an additional refinement step that employs interval-constraint propagation to add information to the abstraction without introducing new grid elements. Moreover, the resulting method allows switching conditions, initial states, and unsafe states to be described by complex constraints, instead of sets that correspond to grid elements. Nevertheless, the method can be easily implemented, since it is based on a well-defined set of constraints, on which one can run any constraint propagation-based solver. Tests of such an implementation are promising.

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Dynamic optimization of interval narrowing algorithms

Cited by 35 publications

References 21 publications

On considering an interval constraint solving algorithm as a free-steering nonlinear Gauss-Seidel procedure

On considering an interval constraint solving algorithm as a free-steering nonlinear Gauss-Seidel procedure

Improvements in computational aspects of interval Kalman filtering enhanced by constraint propagation

Safety verification of hybrid systems by constraint propagation-based abstraction refinement

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