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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Recursive least squares estimation of nonlinear multiple-input systems using orthonormal function expansions.

Georgios D Mitsis1, Marios M Markou

  • 1Department of Electrical and Computer Engineering, University of Cyprus, Nicosia 1678, Cyprus. gmitsis@ucy.ac.cy

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference
|January 19, 2012
PubMed
Summary

This study introduces a computational method for adaptive nonlinear models using function expansions. This approach significantly reduces parameters, improving nonlinear systems identification.

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Area of Science:

  • Systems Engineering
  • Computational Mathematics
  • Signal Processing

Background:

  • Nonlinear systems identification is crucial for understanding complex dynamics.
  • Traditional methods face challenges with parameter explosion in nonlinear models.
  • Volterra-Wiener models offer a framework for nonlinear system representation.

Purpose of the Study:

  • To develop an efficient computational scheme for adaptive nonlinear, multiple-input Volterra-Wiener models.
  • To address the parameter reduction challenge in nonlinear systems identification.
  • To demonstrate the efficacy of function expansions in kernel representation.

Main Methods:

  • Utilizing function expansions for Volterra kernels.
  • Implementing a recursive least-squares formulation.
  • Developing a computational scheme for adaptive model estimation.

Main Results:

  • The proposed scheme successfully obtains adaptive nonlinear models.
  • Function expansions significantly reduce the number of free parameters.
  • Validated performance on a simulated time-varying linear two-input system.

Conclusions:

  • The computational scheme provides an effective method for adaptive nonlinear system modeling.
  • Function expansions are a powerful tool for mitigating parameter complexity.
  • The approach shows promise for identifying systems with time-varying characteristics.