Set inversion via interval analysis for nonlinear bounded-error estimation

Jaulin, Luc; Walter, Éric

doi:10.1016/0005-1098(93)90106-4

Cited by 383 publications

(236 citation statements)

References 13 publications

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“…Here ε is the precision threshold (or the precision for short) of the SM-PE algorithm. The SIVIA (set inversion via interval analysis) algorithm (Jaulin and Walter, 1993) can be cited to exemplify the above principles (branch and bound (bisection) and interval analysis). The number of bisections to be performed is generally prohibitive.…”

Section: Jauberthie Et Almentioning

confidence: 99%

Set-membership identifiability of nonlinear models and related parameter estimation properties

Jauberthie

Travé-MassuyèEs

Verdière

2016

International Journal of Applied Mathematics and Computer Science

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Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, μ-SM-identifiability, and ε-SM-identifiability, to the properties of parameter estimation problems. Soundness and ε-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, μ-SM-identifiability and ε-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.

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Section: Jauberthie Et Almentioning

confidence: 99%

Set-membership identifiability of nonlinear models and related parameter estimation properties

Jauberthie

Travé-MassuyèEs

Verdière

2016

International Journal of Applied Mathematics and Computer Science

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“…This is achieved through constraint reasoning, where initial intervals, representing the uncertainty on parameter values, are safely narrowed by reliable interval methods. Nevertheless, the application of classical constraint approaches to nonlinear inverse problems [53,68] suffer from a major pitfall of considering the same likelihood for all values in the intervals.…”

Section: Nonlinear Inverse Problemsmentioning

confidence: 99%

“…An alternative constraint approach is known as bounded-error estimation or set membership estimation [53,68]. The idea is to replace the search for a single best-fit solution with the characterization of the set of all solutions consistent with acceptable measurement errors around the observations.…”

Section: Classical Techniquesmentioning

confidence: 99%

Probabilistic constraint reasoning

Carvalho¹

2015

Constraints

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perpétuo e sem limites geográficos, de arquivar e publicar esta dissertação através de exemplares impressos reproduzidos em papel ou de forma digital, ou por qualquer outro meio conhecido ou que venha a ser inventado, e de a divulgar através de repositórios científicos e de admitir a sua cópia e distribuição com objectivos educacionais ou de investigação, não comerciais, desde que seja dado crédito ao autor e editor.For Laura with love.My endless source of inspiration with her tender heart and ingenious mind. AcknowledgementsFor me, writing this thesis was like a long, long journey, with many ups and downs. In every step of the way I faced challenges that made me grow as a researcher and as a person. But the journey is coming to an end and is now time to remember and be grateful to those who crossed my path and helped me to achieve my goal in many different ways. Neste trabalho desenvolvemos um paradigma de restrições em domínios contínuos que associa um espaço probabilísticoàs variáveis do problema, permitindo efectuar raciocínio probabilístico. Tal raciocínio baseia-se na avaliação de informação probabilística que requer a computação de integrais multidimensionais em regiões possivelmente não lineares. São desenvolvidos algoritmos capazes de avaliar essa informação, usando técnicas de integração seguras ou aproximadas e dependendo de métodos de programação por restrições em domínios contínuos para obter coberturas da região de integração.A plataforma probabilística de restrições em domínios contínuosé adequada para suporteà decisão em problemas não lineares em domínios contínuos, com incerteza. A sua aplicabilidadeé ilustrada em problemas inversos e problemas de fiabilidade, que são duas classes distintas de problemas de engenharia, representativas do tipo de raciocínio com incerteza requerido pelos decisores.

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“…Set Inversion (SI) (Jaulin and Walter, 1993), a well known paradigm of interval analysis, is well suited approximating solution sets of the form (2) by means of subpavings (sets of nonoverlapping boxes). The problem arises when these sets are of the form (3), because classical Set Inversion is not able to solve this type of problems in a direct way.…”

Section: Quantified Set Inversionmentioning

confidence: 99%

Quantified Set Inversion Algorithm with Applications to Control

et al. 2005

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Abstract. In this paper, a new algorithm based on Set Inversion techniques and Modal Interval Analysis is presented. This algorithm allows solving problems involving quantified constraints over the reals through the characterization of their solution sets. The presented methodology can be applied over a wide range of problems involving uncertain (non)linear systems. Finally, an advanced application is solved.

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Set inversion via interval analysis for nonlinear bounded-error estimation

Cited by 383 publications

References 13 publications

Set-membership identifiability of nonlinear models and related parameter estimation properties

Set-membership identifiability of nonlinear models and related parameter estimation properties

Probabilistic constraint reasoning

Quantified Set Inversion Algorithm with Applications to Control

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