Orthogonal approaches to time-series analysis and system identification

Korenberg, Michael J.; Paarmann, L.D.

doi:10.1109/79.127999

Cited by 120 publications

(36 citation statements)

References 30 publications

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“…Therefore, the DA law doesn't necessarily lead to parameter convergence. This means that the adaptive controller (9) does not necessarily approach the feedback linearization controller (7).…”

Section: B Adaptive Lawmentioning

confidence: 99%

“…Therefore, in this way, and will be close to and , respectively. If other types of approximators are used, e.g., [16], [7], and [4], the parameter initial values must be chosen randomly. In any case, the parameter vectors should be further adjusted by an appropriate adaptive algorithm to be discussed later.…”

Section: A Self-tuning Fuzzy Controllermentioning

confidence: 99%

“…Therefore, the FLSs (2) are qualified as building blocks of nonlinear identification models and nonlinear controllers. Although there are other types of universal approximators such as the simple polynomials [16], orthogonal search approach [7], and the radial basis functions [4], only the FLSs can make use of linguistic information in a systematic way.…”

Section: Fuzzy Logic Systemsmentioning

confidence: 99%

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Hybrid adaptive fuzzy identification and control of nonlinear systems

Hojati

Gazor

2002

IEEE Trans. Fuzzy Syst.

203

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Abstract-In this paper, we present a combined direct and indirect adaptive control scheme for adjusting an adaptive fuzzy controller, and an adaptive fuzzy identification model parameters. First, using adaptive fuzzy building blocks, with a common set of parameters, we design and study an adaptive controller and an adaptive identification model that have been proposed for a general class of the uncertain structure nonlinear dynamic systems. We then propose a hybrid adaptive (HA) law for adjusting the parameters. The HA law utilizes two types of errors in the adaptive system, the tracking error and the modeling error. Performance analysis using a Lyapunov synthesis approach proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence. Furthermore, this is achieved at a negligible increasing in the implementation cost and the computational complexity. We prove a theorem that shows the properties of this hybrid adaptive fuzzy control system, i.e., bounds for the integral of the squared errors, and the conditions under which these errors converge asymptotically to zero are obtained. Finally, we apply the hybrid adaptive fuzzy controller to control a chaotic system, and the inverted pendulum system. The simulation results demonstrate and confirm the theoretical results.

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Section: B Adaptive Lawmentioning

confidence: 99%

Section: A Self-tuning Fuzzy Controllermentioning

confidence: 99%

Section: Fuzzy Logic Systemsmentioning

confidence: 99%

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Hybrid adaptive fuzzy identification and control of nonlinear systems

Hojati

Gazor

2002

IEEE Trans. Fuzzy Syst.

203

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“…is a constant chosen to satisfy a particular confidence interval. For example, to achieve about a 95% confidence interval, would be chosen to equal 4, as seen in inequality #25 in [KOR91]. Choosing a value of 10.9 would yield a confidence interval of about 99.9% [KOR97].…”

Section: Stopping Criterionmentioning

confidence: 99%

Modeling Cooperative Gene Regulation Using Fast Orthogonal Search

Minz¹,

Korenberg²

2008

TOBIOIJ

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A number of computational methods have suggested means by which gene transcription -the process through which RNA is created from DNA -is activated, but there are factors at work that no model has been able to fully explain. In eukaryotes, gene regulation is quite complex, so models have primarily focused on a relatively simple species, Saccharomyces cerevisiae (budding yeast). Because of the inherent complexity in higher species, and even in yeast, a method of identifying transcription factor (TF) binding motifs (specific, short DNA sequences) must be efficient and thorough in its analysis.This thesis shows that a method using the Fast Orthogonal Search (FOS) algorithm to uncover binding motifs as well as cooperatively binding groups of motifs can explain variations in gene expression profiles, which reflect the level at which DNA is transcribed into RNA for a number of genes. The algorithm is very fast, exploring a motif list and constructing a final model within seconds to a few minutes. It produces model terms that are consistent with known motifs, while also revealing new motifs and interactions, and it causes impressive reductions in variance with relatively few model terms over the cell-cycle.iii Co-authorshipPortions of this thesis were co-written along with Michael Korenberg for use in a presently unpublished paper.iv

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“…Volterra Series expansion is widely used in physiology signal estimation and modelling [18][19][20][21][22][23]. For example, Mitsis et al [19] present the insulin-glucose relationship by using the Volterra Model.…”

Section: Related Workmentioning

confidence: 99%

Heart Motion Prediction in Robotic-Assisted Beating Heart Surgery: A Nonlinear Fast Adaptive Approach

Wang

et al. 2013

International Journal of Advanced Robotic Systems

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Off-pump Coronary Artery Bypass Graft (CABG) surgery outperforms traditional on-pump surgery because the assisted robotic tools can alleviate the relative motion between the beating heart and robotic tools. Therefore, it is possible for the surgeon to operate on the beating heart and thus lessens post surgery complications for the patients. Due to the highly irregular and non-stationary nature of heart motion, it is critical that the beating heart motion is predicted in the modelbased track control procedures. It is technically preferable to model heart motion in a nonlinear way because the characteristic analysis of 3D heart motion data through Bi-spectral analysis and Fourier methods demonstrates the involved nonlinearity of heart motion. We propose an adaptive nonlinear heart motion model based on the Volterra Series in this paper. We also design a fast lattice structure to achieve computational-efficiency for realtime online predictions. We argue that the quadratic term of the Volterra Series can improve the prediction accuracy by covering sharp change points and including the motion with sufficient detail. The experiment results indicate that the adaptive nonlinear heart motion prediction algorithm outperforms the autoregressive (AR) and the time-varying Fourier-series models in terms of the root mean square of the prediction error and the prediction error in extreme cases.

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Orthogonal approaches to time-series analysis and system identification

Cited by 120 publications

References 30 publications

Hybrid adaptive fuzzy identification and control of nonlinear systems

Hybrid adaptive fuzzy identification and control of nonlinear systems

Modeling Cooperative Gene Regulation Using Fast Orthogonal Search

Heart Motion Prediction in Robotic-Assisted Beating Heart Surgery: A Nonlinear Fast Adaptive Approach

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