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Nonlinear Model Identification Basics

Identified nonlinear models, black-box modeling, and regularization

Use nonlinear model identification when a linear model does not completely capture your system dynamics. You can identify nonlinear models in the System Identification app or at the command line. System Identification Toolbox™ enables creation and estimation of four nonlinear model structures:

  • Nonlinear ARX models — Represent nonlinearities in your system using dynamic nonlinear mapping objects such as wavelet networks, tree-partitioning, and sigmoid networks.

  • Hammerstein-Wiener models — Estimate static nonlinearities in an otherwise linear system.

  • Nonlinear grey-box models — Represent your nonlinear system using ordinary differential or difference equations (ODEs) with unknown parameters.

  • Neural state-space models — Use neural networks to represent the functions that define the nonlinear state-space realization of your system.

Topics

Nonlinear Identified Models

  • About Identified Nonlinear Models
    Dynamic models in System Identification Toolbox software are mathematical relationships between the inputs u(t) and outputs y(t) of a system.
  • Nonlinear Model Structures
    Construct model objects for nonlinear model structures, access model properties.
  • Available Nonlinear Models
    The System Identification Toolbox software provides four types of nonlinear model structures:
  • Black-Box Modeling
    Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.
  • Types of Model Objects
    Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.

Model Estimation