On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis

Lagrange, Sébastien; Delanoue, Nicolas; Jaulin, Luc

doi:10.1007/s11155-007-9042-9

Cited by 14 publications

(20 citation statements)

References 5 publications

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“…Using the univariate mean value theorem, we observe that maps G that are continuous and have partial derivatives are component-wise D G -affine. See also [14,Theorem 5].…”

Section: Monotonic Maps and Chemical Reaction Networkmentioning

confidence: 99%

Characterizing injectivity of classes of maps via classes of matrices

Feliu

Müller

Regensburger

2019

Linear Algebra and its Applications

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We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of component-wise affine maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vector-valued maps and recent results obtained in the study of chemical reaction networks.

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“…Using the univariate mean value theorem, we observe that maps G that are continuous and have partial derivatives are component-wise D G -affine. See also [14,Theorem 5].…”

Section: Monotonic Maps and Chemical Reaction Networkmentioning

confidence: 99%

Characterizing injectivity of classes of maps via classes of matrices

Feliu

Müller

Regensburger

2019

Linear Algebra and its Applications

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“…The definition of partial injectivity of a function has been introduced in [8]. This notion perfectly characterizes µ-SM-identifiability.…”

Section: Partial Injectivitymentioning

confidence: 99%

“…In order to characterize the global SM-identifiability, the notion of restricted-partial injectivity is introduced. The algorithm proposed in [8], can be easily adapted for testing this new definition. In this definition, A …”

Section: Partial Injectivitymentioning

confidence: 99%

Determination of Set-Membership Identifiability Sets

2014

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Abstract. This paper concerns the concept of set-membership identifiability introduced in [4]. Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely mincing, evaluating and regularization ([6]). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples.

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“…The function q (t) = t 0 v (τ ) dτ (see (1)) is differentiable with respect to t. We can thus apply the generalized mean value theorem (Lagrange, Delanoue, & Jaulin, 2007) on the interval t …”

Section: Injectivity Testmentioning

confidence: 99%

Loop detection of mobile robots using interval analysis

2013

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a b s t r a c tThis paper proposes an original set-membership approach for loop detection of mobile robots in the situation where proprioceptive sensors only are available. To detect loops, the new concepts of the t-plane (which is a two dimensional space with time coordinates) are introduced. Intervals of functions (or tubes) are then used to represent uncertain trajectories and tests are provided in order to eliminate parts of the t-plane that do not correspond to any loop. An experiment with an actual underwater robot is proposed in order to illustrate the principle and the efficiency of the approach.

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On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis

Cited by 14 publications

References 5 publications

Characterizing injectivity of classes of maps via classes of matrices

Characterizing injectivity of classes of maps via classes of matrices

Determination of Set-Membership Identifiability Sets

Loop detection of mobile robots using interval analysis

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