Rigorous parameter reconstruction for differential equations with noisy data

Johnson, Tomas; Tucker, Warwick

doi:10.1016/j.automatica.2008.01.032

Cited by 25 publications

(32 citation statements)

References 15 publications

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“…Since the discretization coefficients may be normalized by any scalar, it can be assumed without loss of generality that monotonic discretizations have β i ≥ 0. From (9) it is immediately clear that if a discretization is monotonic, then any accumulated version of it is also monotonic.…”

Section: Monotonic Discretizationsmentioning

confidence: 99%

“…If one wished to expend the effort to compute a numerical approximation to such a solution, it would be possible to determine directly if it stayed within x. This is the essential idea in the parameter identification approach used in [8,9,11,12,21,22,23,24]. Instead, this scheme simply assumes E j = 0.…”

Section: The Inconsistency Test and Monotonicitymentioning

confidence: 99%

“…As an alternative to the above procedure, parameter bounding schemes have been used [8,9,10,11,12]. The emphasis of these have been the use of interval analysis and Taylor series constraint propagation to guarantee that portions of parameter space are either consistent or inconsistent with the data.…”

Section: Introductionmentioning

confidence: 99%

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Parameter range reduction for ODE models using monotonic discretizations

Willms

Szusz

2013

Journal of Computational and Applied Mathematics

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This paper analyzes the effectiveness of various monotonic discretizations of an ODE in a parameter range reduction algorithm. Several properties of discretizations are given, and five classes of discretizations are defined for various step numbers s. The range reduction algorithm that employs these discretizations is described. Using both analytical results based on the prototypical model x ′ = λx, and empirical results based on two more complicated models, it is shown that one particular class of discretizations (the A1OUT class) results in the tightest bounds on the parameters. This result is shown to be attributed to a certain characteristic value, A 0 , of the discretization. Accumulation of these discretizations is also defined, and its usefulness in the range reduction algorithm is described.

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Section: Monotonic Discretizationsmentioning

confidence: 99%

Section: The Inconsistency Test and Monotonicitymentioning

confidence: 99%

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Parameter range reduction for ODE models using monotonic discretizations

Willms

Szusz

2013

Journal of Computational and Applied Mathematics

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“…The methods based in interval analysis were extended to models described by differential equations as seen in [5], [7], [9], and [10].…”

Section: Bounded Error Parameter Identificationmentioning

confidence: 99%

Bounded error parameter estimation for models described by ordinary and delay differential equations

Burns

Childers

2009

2009 17th Mediterranean Conference on Control and Automation

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“…This is a standard inverse problem, and many methods for finding solutions to this problem have been developed to date (sensitivity functions [20], splines [6], interval analysis [15], adaptive observers [19], [5], [9], [12], [24], [25], [8] and particle filters and Bayesian inference methods [1]). Despite these methods are based on different mathematical frameworks, they share a common feature: one is generally required to repeatedly find numerical solutions of nonlinear ordinary differential equations (ODEs) over given intervals of time (solve the direct problem).…”

Section: Introductionmentioning

confidence: 99%