Notes on Triangular Sets and Triangulation-Decomposition Algorithms I: Polynomial Systems

Hubert, Evelyne

doi:10.1007/3-540-45084-x_1

Cited by 66 publications

(84 citation statements)

References 30 publications

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“…For fixed k, , the question can be formulated in terms of differential polynomial rings: does the differential ideal generated by left-hand sides of the equations (49) contain the polynomials ED i p ? Differential elimination (see [20] or the recent survey [13]) is relevant here; finite algorithms have been already implemented in computer algebra. Although we have not yet succeeded (because of complexity) in carrying out these computations, even on example (49) for (k, ) = (3, 4), and although it will certainly not provide a bound on k, , we do believe that computer algebra is a considerable potential help.…”

Section: Resultsmentioning

confidence: 99%

“…Le us illustrate the computation of S, T and J on the following three particular cases of (3). For each of them, the table below gives the differential forms ω and η, the decomposition of dω ∧ ω on ω 1 , ω, η, dλ and the resulting S, T, J according to (13). System (a) was already studied in Example 2.4.…”

Section: The Functions S T and Jmentioning

confidence: 99%

“…From (13), it means that the Lie derivative of ω along ∂/∂λ is co-linear to ω, and this is classically equivalent to a decomposition ω = kω 2 where k = 0 is a function of the four variables x, y, x, λ butω 2 is a differential form in the three variables x, y, z, the first integrals of ∂/∂λ. Then, one can prove that the form ω 3 = ω 3 /k and the functionâ 0 = a 0 /k also involve the variables x, y, z only.…”

Section: Z) It Is Obvious That Any T → (U(t) V(t) X(t) Y(t) Z(t)mentioning

confidence: 99%

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Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

Avanessoff

Pomet

2007

ESAIM: COCV

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Abstract. This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about "(x, u)-flatness" of these systems, with much more elementary techniques.Mathematics Subject Classification. 93B18, 93B29, 34C20.

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Section: Resultsmentioning

confidence: 99%

Section: The Functions S T and Jmentioning

confidence: 99%

Section: Z) It Is Obvious That Any T → (U(t) V(t) X(t) Y(t) Z(t)mentioning

confidence: 99%

See 1 more Smart Citation

Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

Avanessoff

Pomet

2007

ESAIM: COCV

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“…Complete lecture notes [25,26] are available for a detailed understanding of the concepts involved and the algorithms underlying the diffalg library in Maple. A representative sample of the original articles is [6,7,24,38,41,55,56] All these address systems of classical differential equations, i.e.…”

Section: Generalized Differential Algebrasmentioning

confidence: 99%

“…The Maple library diffalg was extended to handle this new type of differential polynomial ring [5,27]. The concepts and algorithms underlying it are described in great details in [25,26].…”

Section: Generalized Differential Algebrasmentioning

confidence: 99%

Algebraic and Differential Invariants

Hubert¹

2012

Foundations of Computational Mathematics, Budapest 2011

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Global Identifiability of Differential Models

Hong

Ovchinnikov

Pogudin

et al. 2020

Comm Pure Appl Math

112

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Many real‐world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and output data. The main contribution of this paper is to provide theory, an algorithm, and software for deciding global identifiability. First, we rigorously derive an algebraic criterion for global identifiability (this is an analytic property), which yields a deterministic algorithm. Second, we improve the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. With our new algorithm, we can tackle problems that could not be tackled before. A software based on the algorithm (called SIAN) is available at https://github.com/pogudingleb/SIAN. © 2020 Wiley Periodicals LLC

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Notes on Triangular Sets and Triangulation-Decomposition Algorithms I: Polynomial Systems

Cited by 66 publications

References 30 publications

Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

Algebraic and Differential Invariants

Global Identifiability of Differential Models

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