Applied Interval Analysis

By L. Jaulin, M. Kieffer, Olivier Didrit, Éric Walter. Springer London, 2001

1,951 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/60ed3b3b10f9d9814cc823bbb16114f5795ad5d0

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Citations in the corpus

Solving the Forward Kinematics of a Gough-Type Parallel Manipulator with Interval Analysis (2004, methodology): “Constraint propagation (Jaulin et al. 2001) is a classical method in the field of interval analysis.”
Minimum-time trajectory planning of mechanical manipulators under dynamic constraints (2002, methodology): “More details on the applications of interval analysis to algorithms for global optimization can be found in Hansen (1992), Ratschek and Rokne (1988) and Jaulin et al. (2001).”
GUARANTEED NONLINEAR STATE ESTIMATION FOR CONTINUOUS-TIME DYNAMICAL MODELS FROM DISCRETE-TIME MEASUREMENTS (2006, background): “The main difficulty is to obtain suitable functions ω (·) and Ω (·).”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, background): “To handle this situation, it is possible to ‘protect’ the estimator against a prespecified number of outliers, by allowing for a number of output variables to be outside of their prior feasible intervals (see, e.g., Jaulin et al., 2001; Kieffer and Walter, 2005).”
Survey of sampling-based methods for uncertainty and sensitivity analysis (2006, background): “Alternative representations for uncertainty such as evidence theory and possibility theory merit consideration for their potential to represent uncertainty in situations where little information is available [84–92].”
Standardized notation in interval analysis (2010, background): “We hope that the suggested notation will appear persuasive to authors in interval analysis and its applications, convincing them that using it is likely to improve the communication of ideas in interval analysis to colleagues and potential users.”
Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence (2015, background): “…1966) has also led to state bounding algorithms, either based on set predictions/intersections (Chisci, Garulli, & Zappa, 1996; Combastel, 2003; Jaulin et al., 2001; Raïssi, Ramdani, & Candau, 2004) resembling Kalman filtering, or based on interval observers (Combastel, 2013; Gouzé, Rappaport,…”
Experimental uncertainty estimation and statistics for data having interval uncertainty. (2007, methodology): “…of the repeated parameters, such as replacing the original expression x + x + x with the equivalent expression 3x, or completing the square (Jaulin et al. 2001) by which x + x2 is re-expressed as (x + ½ )2 − ¼ , which looks a bit more complex but has only one instance of the uncertain…”