On the identifiability of the time delay with least-squares methods

Ferretti, Gianni; Maffezzoni, C.; Scattolini, Riccardo

doi:10.1016/0005-1098(95)00172-7

Cited by 30 publications

(29 citation statements)

References 7 publications

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“…The optimization procedure minimized the objective function using the Levenberg-Marquardt algorithm (Moré, 1978), implemented with MATLAB's lsqcurvefit function (MATLAB, MathWorks, Natick, MA, USA). To avoid convergence problems associated with parameter optimization in time-delayed dynamical systems, we visually estimated each trial's time delay rather than treating it as a parameter to be optimized (Ferretti et al, 1996;Müller et al, 2003).…”

Section: Discussionmentioning

confidence: 99%

Fast and slow processes underlie the selection of both step frequency and walking speed

Pagliara

Snaterse

Donelan

2014

Journal of Experimental Biology

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People prefer gaits that minimize their energetic cost. Research focused on step frequency selection suggests that a fast predictive process and a slower optimization process underlie this energy optimization. Our purpose in this study was to test whether the mechanisms controlling step frequency selection are used more generally to select one of the most relevant characteristics of walking -preferred speed. To accomplish this, we contrasted the dynamic adjustments in speed following perturbations to step frequency against the dynamic adjustments in step frequency following perturbations to speed. Despite the use of different perturbations and contexts, we found that the responses were very similar. In both experiments, subjects responded to perturbations by first rapidly changing their speed or step frequency towards their preferred pattern, and then slowly adjusting their gait to converge onto their preferred pattern. We measured similar response times for both the fast processes (1.4±0.3 versus 2.7±0.6 s) and the slow processes (74.2±25.4 versus 79.7±20.2 s). We also found that the fast process, although quite variable in amplitude, dominated the adjustments in both speed and step frequency. These distinct but complementary experiments demonstrate that people appear to rely heavily on prediction to rapidly select the most relevant aspects of their preferred gait and then gradually fine-tune that selection, perhaps using direct optimization of energetic cost.

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Section: Discussionmentioning

confidence: 99%

Fast and slow processes underlie the selection of both step frequency and walking speed

Pagliara

Snaterse

Donelan

2014

Journal of Experimental Biology

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“…In addition, the choice of the model structure (order and time delay) and the parameter estimation are two basic elements in the identification problem. Therefore, lots of works that used various methods to estimate the time delay and the order model have been published in the literature [15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Section: Preliminary Studymentioning

confidence: 99%

“…However, it is assumed to be negligible in several researches, in order to simplify the study. To overcome this assumption, a variety of algorithms are introduced into the time-delay estimation, in order to improve the precision and the convergence in the modeling, identification, and control processes [23][24][25][26][27][28]. The time-delay identification is a greatly studied problem with several works in the literature.…”

Section: Time-delay Estimationmentioning

confidence: 99%

Improved Discrete Techniques of Time‐Delay and Order Estimation for Large‐Scale Interconnected Nonlinear Systems

Elloumi

Kamoun

2017

Mathematical Problems in Engineering

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The selection of a suitable model structure is an essential step in system modeling. Model structure is defined by determining the class, the time delay, and the model order. This paper proposes improved structural estimation procedures for large-scale interconnected nonlinear systems which are composed of a set of interconnected Single-Input Single-Output (SISO) Hammerstein structures and described by discrete-time stochastic models with unknown time-varying parameters. An extensive Determinant Report (DR) algorithm is developed to determine the order of the process. An improved discrete-time technique based on Recursive Extended Least Squares with Varying Time (RELSVT) delay method is proposed to estimate the time delays of the considered system. The developed theoretical analysis and simulation results prove the validity and performance of the proposed algorithms.

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“…The time-delay is a continuous parameter, and all parameters are estimated by a prediction error/maximum likelihood method, using iterative search [23]. It is well known that the objective function may have many local minima in this case, [8,26,29], so the initialization of the parameters must be done with great care. Here we use an initialization method implemented in [24], based on ARXS (see below), followed by a global search for best time delay and model zero for fixed poles, followed by local Gauss-Newton search for all free parameters.…”

Section: 23mentioning

confidence: 99%

“…Here we use an initialization method implemented in [24], based on ARXS (see below), followed by a global search for best time delay and model zero for fixed poles, followed by local Gauss-Newton search for all free parameters. Other ideas how to handle the problem of local minima are described in [8].…”

Section: 23mentioning

confidence: 99%

A review of time-delay estimation techniques

Björklund

Ljung

42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)

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On the identifiability of the time delay with least-squares methods

Cited by 30 publications

References 7 publications

Fast and slow processes underlie the selection of both step frequency and walking speed

Fast and slow processes underlie the selection of both step frequency and walking speed

Improved Discrete Techniques of Time‐Delay and Order Estimation for Large‐Scale Interconnected Nonlinear Systems

A review of time-delay estimation techniques

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