Nonlinear ARX Models - MATLAB & Simulink - MathWorks América Latina (2025)

Nonlinear behavior modeled using dynamic networks such as sigmoid and wavelet

Use nonlinear ARX models to represent nonlinearities in your system using dynamic nonlinearity estimators such as wavelet networks, tree-partitioning, and sigmoid networks. In the toolbox, these models are represented as idnlarx objects. You can estimate Nonlinear ARX models in theSystem Identificationapp, or at the command line using thenlarxcommand.

Apps

System IdentificationIdentify models of dynamic systems from measured data

Functions

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idnlarxNonlinear ARX model
nlarxEstimate parameters of nonlinear ARX model
nlarxOptionsOption set for nlarx
isnlarxDetect nonlinearity in estimation data
initSet or randomize initial parameter values
getpvecObtain model parameters and associated uncertainty data
setpvecModify values of model parameters
linearRegressorSpecify linear regressor for nonlinear ARX model (Since R2021a)
polynomialRegressorSpecify polynomial regressor for nonlinear ARX model (Since R2021a)
periodicRegressorSpecify periodic regressor for nonlinear ARX model (Since R2022a)
customRegressorSpecify custom regressor for nonlinear ARX model (Since R2021a)
getregRegressor expressions and numerical values in nonlinear ARX model
polyreg(Not recommended) Powers and products of standard regressors
customreg(Not recommended) Custom regressor for nonlinear ARX models
addreg(Not recommended) Add custom regressors to nonlinear ARX model
idWaveletNetworkWavelet network function for nonlinear ARX and Hammerstein-Wiener models
idSigmoidNetworkSigmoid network function for nonlinear ARX and Hammerstein-Wiener models
idTreePartitionTree-partitioned nonlinear function for nonlinear ARX models
idCustomNetworkCustom network function for nonlinear ARX and Hammerstein-Wiener models
idLinearLinear mapping object for nonlinear ARX models
idGaussianProcessGaussian process regression mapping function for nonlinear ARX and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox) (Since R2021b)
idTreeEnsembleDecision tree ensemble mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox) (Since R2021b)
idSupportVectorMachineSupport vector machine regression mapping function for nonlinear ARX models (requires Statistics and Machine Learning Toolbox) (Since R2022a)
idNeuralNetworkMultilayer neural network mapping function for nonlinear ARX models and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox or Deep Learning Toolbox) (Since R2023b)
idFeedforwardNetwork(Not recommended) Multilayer feedforward neural network mapping function for nonlinear ARX models (requires Deep Learning Toolbox)
evaluateEvaluate output values of idnlarx or idnlhw mapping object array for given set of input values
simSimulate response of identified model
simOptionsOption set for sim
predictPredict identified model K-step-ahead output
predictOptionsOption set for predict
compareCompare identified model output with measured output
compareOptionsOption set for compare
forecastForecast identified model output
forecastOptionsOption set for forecast
nlarxPlotPlot nonlinearity of nonlinear ARX model (Since R2023a)
evaluateEvaluate output values of idnlarx or idnlhw mapping object array for given set of input values
getDelayInfoGet input/output delay information for idnlarx model structure
idnlarx/findopCompute operating point for Nonlinear ARX model
findopOptionsOption set for findop
idnlarx/operspecConstruct operating point specification object for idnlarx model
idnlarx/linearizeLinearize nonlinear ARX model
linappLinear approximation of nonlinear ARX and Hammerstein-Wiener models for given input

Blocks

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Nonlinear ARX ModelSimulate nonlinear ARX model in Simulink software
Iddata SinkExport simulation data as iddata object to MATLAB workspace
Iddata SourceImport time-domain data stored in iddata object in MATLAB workspace

Topics

  • What are Nonlinear ARX Models?

    Understand the structure of a nonlinear ARX model.

  • Available Mapping Functions for Nonlinear ARX Models

    Choose from sigmoid, wavelet, tree partition, linear,neural, and custom network nonlinearities.

  • Identifying Nonlinear ARX Models

    Specify the Nonlinear ARX structure, and configurethe estimation algorithm.

    • Identify Nonlinear Black-Box Models Using System Identification App
    • Estimate Nonlinear ARX Models at the Command Line
    • Estimate Nonlinear ARX Models Initialized Using Linear ARX Models
  • Validate Nonlinear ARX Models

    Plot model nonlinearities, analyze residuals, andsimulate and predict model output.

  • Using Nonlinear ARX Models

    Simulate, predict, and forecast model output, linearizenonlinear ARX models, and import estimated models into the Simulink® software.

  • Linear Approximation of Nonlinear Black-Box Models

    Choose the approach for computing linear approximations, compute operating points for linearization, and linearize your model.

  • How the Software Computes Nonlinear ARX Model Output

    How the software evaluates the output of nonlinearityestimators and uses this output to compute the model response.

Featured Examples

A Tutorial on Identification of Nonlinear ARX and Hammerstein-Wiener ModelsIdentify single-input-single-output (SISO) nonlinear black box models using measured input-output data.

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Create Black-Box Models of a Robotic Arm System Using Neural NetworksUse neural networks as the nonlinear function when you model nonlinear ARX and Hammerstein-Wiener models. It compares the nonlinear systems estimated using different types of neural networks, activation functions, and number of layers.
Building Nonlinear ARX Models with Nonlinear and Custom RegressorsUse custom regressors in SISO and MIMO nonlinear ARX (IDNLARX) models.

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Machine-Learning-Based Identification of Two-Tank SystemIdentify a black-box dynamic model of a nonlinear two-tank system using machine learning.

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Machine-Learning-Based Identification of Nonlinear Magneto-Rheological Fluid DamperEstimate a black-box dynamic model of a nonlinear magneto-rheological (MR) fluid damper using machine learning.

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Surrogate Modeling Using Gaussian Process-Based NLARX ModelIn this example, you replace a hydraulic cavitation cycle model in Simulink with a surrogate nonlinear ARX (NLARX) model to facilitate faster simulation.

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Piezoelectric Actuator Model Identification Using Machine LearningIdentify a piezoelectric actuator nonlinear model using machine-learning-based techniques that include support vector machines and Gaussian process functions.

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Nonlinear ARX Model of SI Engine Torque DynamicsDescribes modeling the nonlinear torque dynamics of a spark-ignition (SI) engine as a nonlinear ARX model. The identified model can be used for hardware-in-the-loop (HIL) testing, powertrain control, diagnostic, and training algorithm design. For example, you can use the model for aftertreatment control and diagnostics algorithm development. For more information on nonlinear ARX models, see Nonlinear ARX Models.

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Nonlinear ARX Models
- MATLAB & Simulink
- MathWorks América Latina (2025)
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