customRegressor

Specify custom regressor for nonlinear ARX model

Description

A custom regressor represents a single user-provided formula that operates on delayed input and output variables. For example, y(t–1)eu(t–1) is a custom regressor that you can construct using the formula `@(x,y)x.*exp(y)`. A `customRegressor` object encapsulates a set of custom regressors. Use `customRegressor` objects when you create nonlinear ARX models using `idnlarx` or `nlarx`. You can specify `customRegressor` objects along with `linearRegressor` and `polynomialRegressor` objects and combine them into a single combined regressor set.

Creation

Syntax

``cReg = customRegressor(Variables,Lags,Fcn)``
``cReg = customRegressor(Variables,Lags,Fcn,Vectorized)``

Description

example

````cReg = customRegressor(Variables,Lags,Fcn)` creates a `customRegressor` object, with the output and input names in `Variables`, the corresponding lags in `Lags`, and the function handle in `Fcn`. `Fcn` sets the `VariablesToRegressorFcn` property. For example, if `Variables` contains `'y'`, `lags` contains the corresponding lag vector ```[2 4]```, and the custom function is `@(x)sin(x)`, then the regressors that use `'y'` are sin(y(t–2)) and sin(y(t–4)).```
````cReg = customRegressor(Variables,Lags,Fcn,Vectorized)` specifies whether `Fcn` can process a vector of inputs to return a vector of output values, based on the value of `Vectorized`.```

Properties

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Custom function that transforms a set of delayed variables into a numeric scalar output, specified as a function handle.

Example: `@(x)sin(x)`

Example: `@(x,y)x.*exp(y)`

Output and input variable names, specified as a cell array of strings or a cell array that references the `OutputName` and `InputName` properties of an `iddata` object. Each entry must be a string with no special characters other than white space.

Example: `{'y1','u1'}`

Example: `[z.OutputName; z.InputName]`

Lags in each variable, specified as a 1-by-nv cell array of non-negative integer row vectors, where nv is the total number of regressor variables. Each row vector contains nr integers that specify the nr regressor lags for the corresponding variable. When nr>1 for at least one of the variables, then the software generates a regressor for every lag combination. For instance, suppose that you want to create the formula r(t) = sin(y1(ta))cos(u1(tb)), where lag a can be `1` or `2` and lag b can be `0` or `3`. Specify `Lags` as `{[1 2],[0 3]}`, which corresponds to the variables `{'y1','u1'}`. This specification creates the following set of regressors:

• `'sin(y1(t-1))*cos(u1(t))'`

• `'sin(y1(t-1))*cos(u1(t-3))'`

• `'sin(y1(t-2))*cos(u1(t))'`

• `'sin(y1(t-2))*cos(u1(t-3))'`

If a lag corresponds to an output variable of an `idnlarx` model, the minimum lag must be greater than or equal to 1.

Example: `{1 1}`

Example: `{[1 2],[1,3,4]}`

Vectorization indicator that determines whether `VariablesToRegressorFcn` is vectorized , specified as `true` or `false`.

For an example of setting this property, see Use Absolute Value in Polynomial Regressor Set.

Example: `[true,false]`

Name of the time variable, specified as a valid MATLAB® variable name that is distinct from values in `Variables`.

Example: `'ClockTime'`

Examples

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Create a custom regressor that represents the formula $\mathit{x}{\mathit{e}}^{\mathit{y}}$.

Specify the input variables as `'u1`' and `'y1`' and corresponding lags of `1` and `3` delays.

```vars = {'y1','u1'}; lags = {1 3};```

Specify the custom function.

`fcn = @(x,y)x.*exp(y);`

Create the regressor.

`cReg = customRegressor(vars,lags,fcn)`
```cReg = Custom regressor: y1(t-1).*exp(u1(t-3)) VariablesToRegressorFcn: @(x,y)x.*exp(y) Variables: {'y1' 'u1'} Lags: {[1] [3]} Vectorized: 1 TimeVariable: 't' Regressors described by this set ```

Create a set of custom regressors in three variables, all based on the formula $\mathit{xy}+\mathrm{sin}\left(\mathit{z}\right)$.

Specify the variable names and the lags.

```vars = {'a','b','c'}; lags = {[1 5],[0 8],7};```

Specify the custom function.

`fcn = @(x,y,z)x.*y+sin(z);`

Create the custom regressor set.

`cReg = customRegressor(vars,lags,fcn)`
```cReg = Custom regressor: @(x,y,z)x.*y+sin(z) VariablesToRegressorFcn: @(x,y,z)x.*y+sin(z) Variables: {'a' 'b' 'c'} Lags: {[1 5] [0 8] [7]} Vectorized: 1 TimeVariable: 't' Regressors described by this set ```

`cReg` specifies regressors for all possible lag combinations.

Load the estimation data `z1`, which has one input and one output, and obtain the output and input names.

```load iddata1 z1; names = [z1.OutputName z1.InputName]```
```names = 1×2 cell {'y1'} {'u1'} ```

Specify `L` as the set of linear regressors that represents ${\mathit{y}}_{1}\left(\mathit{t}-1\right)$, ${\mathit{u}}_{1}\left(\mathit{t}-2\right)$, and ${\mathit{u}}_{1}\left(\mathit{t}-5\right)$.

`L = linearRegressor(names,{1,[2 5]});`

Specify `P` as the polynomial regressor ${{\mathit{y}}_{1}\left(\mathit{t}-1\right)}^{2}$.

`P = polynomialRegressor(names(1),1,2);`

Specify `C` as the custom regressor ${\mathit{y}}_{1}\left(\mathit{t}-2\right)$${\mathit{u}}_{1}\left(\mathit{t}-3\right)$. Use an anonymous function handle to define this function.

`C = customRegressor(names,{2 3},@(x,y)x.*y)`
```C = Custom regressor: y1(t-2).*u1(t-3) VariablesToRegressorFcn: @(x,y)x.*y Variables: {'y1' 'u1'} Lags: {[2] [3]} Vectorized: 1 TimeVariable: 't' Regressors described by this set ```

Combine the regressors in the column vector `R`.

`R = [L;P;C]`
```R=3×1 object [3 1] array of linearRegressor, polynomialRegressor, customRegressor objects. ------------------------------------ 1. Linear regressors in variables y1, u1 Variables: {'y1' 'u1'} Lags: {[1] [2 5]} UseAbsolute: [0 0] TimeVariable: 't' ------------------------------------ 2. Order 2 regressors in variables y1 Order: 2 Variables: {'y1'} Lags: {[1]} UseAbsolute: 0 AllowVariableMix: 0 AllowLagMix: 0 TimeVariable: 't' ------------------------------------ 3. Custom regressor: y1(t-2).*u1(t-3) VariablesToRegressorFcn: @(x,y)x.*y Variables: {'y1' 'u1'} Lags: {[2] [3]} Vectorized: 1 TimeVariable: 't' Regressors described by this set ```

Estimate a nonlinear ARX model with `R`.

`sys = nlarx(z1,R)`
```sys = Nonlinear ARX model with 1 output and 1 input Inputs: u1 Outputs: y1 Regressors: 1. Linear regressors in variables y1, u1 2. Order 2 regressors in variables y1 3. Custom regressor: y1(t-2).*u1(t-3) List of all regressors Output function: Wavelet Network with 1 unit Sample time: 0.1 seconds Status: Estimated using NLARX on time domain data "z1". Fit to estimation data: 59.73% (prediction focus) FPE: 3.356, MSE: 3.147 ```

View the full regressor set.

`getreg(sys)`
```ans = 5×1 cell {'y1(t-1)' } {'u1(t-2)' } {'u1(t-5)' } {'y1(t-1)^2' } {'y1(t-2).*u1(t-3)'} ```