Learn more about System Identification Toolbox

linear - Specify to estimate nonlinear ARX model that is linear in (nonlinear) custom regressors

Syntax

lin=linear lin=linear('Parameters',Par)

Description

linear is an object that specifies that the nonlinear ARX model is linear in custom (nonlinear) regressors. You define custom regressors using customreg.

lin=linear instantantiates the linear object.

lin=linear('Parameters',Par) instantantiates the linear object and specifies optional values in the Par structure. For more information about this structure, see linear Properties.

Remarks

linear is a linear (affine) function , defined as follows:

y is scalar, and x is a 1-by-m vector.

Use evaluate(lin,x) to compute the value of the function defined by the linear object lin at x.

linear Properties

You can include property-value pairs in the constructor to specify the object.

After creating the object, you can use get or dot notation to access the object property values. For example:

% List Parameters values
get(lin)
% Get value of Parameters property
lin.Parameters

Property Name Description

Property Name	Description
`Parameters`	Structure containing the following fields: `LinearCoef`: `m`-by-1 vector L. `OutputOffset`: Scalar `d`.

Parameters

Structure containing the following fields:

LinearCoef: m-by-1 vector L.
OutputOffset: Scalar d.

Examples

To specify that the nonlinear ARX model is linear in custom regressors, first specify one or more customreg objects. Then, include the linear object in the nlarx estimator command.

For example, to estimate a nonlinear ARX model linear in the custom regressors, use the following syntax:

m=nlarx(Data,Orders,linear,'custom',{'y(t-1)*u(t-2)'});

Note In this example, the custom regressor is a nonlinear function of input and output variables.

Algorithm

When the idnlarx property Focus is 'Prediction', linear uses a fast, noniterative initialization and iterative search technique for estimating parameters. In most cases, iterative search requires only a few iterations.

When the idnlarx property Focus='Simulation', linear uses an iterative technique for estimating parameters.