Nonlinear Model Structures

About System Identification Toolbox Model Objects

Objects are instances of model classes. Each class is a blueprint that defines the following information about your model:

How the object stores data
Which operations you can perform on the object

This toolbox includes nine classes for representing models. For example, idss represents linear state-space models and idnlarx represents nonlinear ARX models. For a complete list of available model objects, see Available Linear Models and Available Nonlinear Models.

Model properties define how a model object stores information. Model objects store information about a model, such as the mathematical form of a model, names of input and output channels, units, names and values of estimated parameters, parameter uncertainties, and estimation report. For example, an idss model has an InputName property for storing one or more input channel names.

The allowed operations on an object are called methods. In System Identification Toolbox™ software, some methods have the same name but apply to multiple model objects. For example, step creates a step response plot for all dynamic system objects. However, other methods are unique to a specific model object. For example, canon is unique to state-space idss models and linearize to nonlinear black-box models.

Every class has a special method, called the constructor, for creating objects of that class. Using a constructor creates an instance of the corresponding class or instantiates the object. The constructor name is the same as the class name. For example, idss and idnlarx are both the name of the class and the name of the constructor for instantiating the linear state-space models and nonlinear ARX models, respectively.

When to Construct a Model Structure Independently of Estimation

You use model constructors to create a model object at the command line by specifying all required model properties explicitly.

You must construct the model object independently of estimation when you want to:

Simulate or analyze the effect of model parameters on its response, independent of estimation.
Specify an initial guess for specific model parameter values before estimation. You can specify bounds on parameter values, or set up the auxiliary model information in advance, or both. Auxiliary model information includes specifying input/output names, units, notes, user data, and so on.

In most cases, you can use the estimation commands to both construct and estimate the model—without having to construct the model object independently. For example, the estimation command tfest creates a transfer function model using data and the number of poles and zeros of the model. Similarly, nlarx creates a nonlinear ARX model using data and model orders and delays that define the regressor configuration. For information about how to both construct and estimate models with a single command, see Model Estimation Commands.

In case of grey-box models, you must always construct the model object first and then estimate the parameters of the ordinary differential or difference equation.

Commands for Constructing Nonlinear Model Structures

The following table summarizes the model constructors available in the System Identification Toolbox product for representing various types of nonlinear models.

After model estimation, you can recognize the corresponding model objects in the MATLAB^® Workspace browser by their class names. The name of the constructor matches the name of the object it creates.

For information about how to both construct and estimate models with a single command, see Model Estimation Commands.

Summary of Model Constructors

Model Constructor	Resulting Model Class
`idnlgrey`	Nonlinear ordinary differential or difference equation (grey-box models). You write a function or MEX-file to represent the governing equations.
`idnlarx`	Nonlinear ARX models, which define the predicted output as a nonlinear function of past inputs and outputs.
`idnlhw`	Nonlinear Hammerstein-Wiener models, which include a linear dynamic system with nonlinear static transformations of inputs and outputs.
`idNeuralStateSpace`	Neural state-space models, which use neural networks to approximate the functions representing a nonlinear state space realization of your system.

For more information about when to use these commands, see When to Construct a Model Structure Independently of Estimation.

Model Properties

A model object stores information in the properties of the corresponding model class.

The nonlinear models idnlarx, idnlhw, and idnlgrey are based on the idnlmodel superclass and inherit all idnlmodel properties.

In general, all model objects have properties that belong to the following categories:

Names of input and output channels, such as InputName and OutputName
Sample time of the model, such as Ts
Time units
Model order and mathematical structure (for example, ODE or nonlinearities)
Properties that store estimation results (Report)
User comments, such as Notes and Userdata

For information about getting help on object properties, see the model reference pages.

The following table summarizes the commands for viewing and changing model property values. Property names are not case sensitive. You do not need to type the entire property name if the first few letters uniquely identify the property.

Task	Command	Example
View all model properties and their values	Use `get`.	Load sample data, compute a nonlinear ARX model, and list the model properties. load iddata1 sys = nlarx(z1,[4 4 1]); get(sys)
Access a specific model property	Use dot notation.	View the output function in the previous model. sys.OutputFcn
Access a specific model property	For properties, such as `Report`, that are configured like structures, use dot notation of the form `model.PropertyName.FieldName`. `FieldName` is the name of any field of the property.	View the options used in the nonlinear ARX model estimation. sys.Report.OptionsUsed
Change model property values	Use dot notation.	Change the nonlinearity mapping function that the output function uses. sys.OutputFcn = 'idSigmoidNetwork';
Access model parameter values and uncertainty information	Use `getpvec` and `getcov` (for `idnlgrey` models only).	Model parameters and associated uncertainty data. getpvec(sys)
Set model parameter values and uncertainty information	Use `setpar` and `setcov` (for `idnlgrey` models only).	Set the parameter vector. sys = setpar(sys,'Value',parlist)
Get number of parameters	Use `nparams`.	Get the number of parameters. nparams(sys)