idNeuralStateSpace - Neural state-space model with identifiable network weights (2024)

nx — Number of state variables
positive integer

State function network, specified as a dlnetwork (Deep Learning Toolbox) object. This network approximates the state function of the state-space system (F). For continuous state-space systems the state function returns the system state derivative with respect to time, while for discrete-time state-space systems it returns the next state. The inputs of the function are time (if IsTimeInvariant is false), the current state, and the current input (if NumInputs is positive), in that order.

When an idNeuralStateSpace model is constructed, a default state network is created. It is a multi-layer perceptron (MLP) network with the following features:

To change the default network configuration, use createMLPNetwork. For example:

 nss.StateNetwork = createMLPNetwork(nss,"state",... LayerSizes=[64 64 64],...  Activations="sigmoid")

You can also directly assign a custom dlnetwork object as the state function network when the sizes of the input layers are distinguishable. For example:

nss.StateNetwork = dlnet;

where dlnet is a custom dlnetwork object with the configuration as mentioned under the dlnet argument in setNetwork.

For more information on custom networks and how to assign them to an idNeuralStateSpace object when the input layer sizes are not distinguishable, see setNetwork.

To train both state and output networks, use nlssest. For example:

 options1 = nssTrainingOptions("adam"); nss = nlssest(U, Y, nss, options1);

Output function networks, specified as a 2-by-1 array of dlnetwork (Deep Learning Toolbox) objects. The first network represents the identity relation between y₁ and x, since all the states are measured. This network has no learnable parameters, is fixed, and cannot be changed or trained.

The second network approximates the output function H of the state-space system, which is a function of time (if IsTimeInvariant is false), the current state, and the current input (if NumInputs is positive and HasFeedthrough is true), in that order.

When you create an idNeuralStateSpace model, the default network created to approximate H is a multi-layer perceptron (MLP) network with the following features:

To change the default network configuration, use createMLPNetwork. For example:

 nss.OutputNetwork = createMLPNetwork(nss,"output",... LayerSizes=[64 64 64],...  Activations="sigmoid")

You can also directly assign a custom dlnetwork object as the output function network when the sizes of the input layers are distinguishable. For example:

nss.OutputNetwork = dlnet;

where dlnet is a custom dlnetwork object with the configuration as mentioned under the dlnet argument in setNetwork.

For more information on custom networks and how to assign them to an idNeuralStateSpace object when the input layer sizes are not distinguishable, see setNetwork.

To train both state and output networks, use nlssest. For example:

options1 = nssTrainingOptions("adam")options2 = nssTrainingOptions("sgdm")nss = nlssest(U, Y, nss, [options1; options2])

Encoder function network, specified as a dlnetwork (Deep Learning Toolbox) object. The encoder maps the state to a latent state (usually, of a lower dimension), which is the input to the state function network. The dimension of this latent state is specified by LatentDim.

The default value is [], which means that you are not using the encoder. You add an encoder to your model by changing the default value of LatentDim. This encoder network, by default contains two layers of size 64 with tanh as the activation function.

To change the default encoder network configuration, use createMLPNetwork. For example:

 nss.Encoder = createMLPNetwork(nss,"encoder",... LayerSizes=[4 4],...  Activations="sigmoid")

You can also directly assign a custom dlnetwork object as the encoder function network. For example:

nss.Encoder = dlnet;

where dlnet is a custom dlnetwork object with one input representing the original state and one output representing the latent state.

For more information on autoencoders, see What are Neural State-Space Models?

Decoder function network, specified as a dlnetwork (Deep Learning Toolbox) object. The output of the state function network is the input of the decoder. The decoder maps the latent state back to the original state. The dimension of the latent state is specified by LatentDim.

The default value is [], which means that you are not using the decoder. You add a decoder to your model by changing the default value of LatentDim. This decoder network, by default, contains two layers of size 64 with tanh as the activation function.

To change the default decoder network configuration, use createMLPNetwork. For example:

 nss.Decoder = createMLPNetwork(nss,"decoder",... LayerSizes=[4 4],...  Activations="sigmoid")

You can also directly assign a custom dlnetwork object as the decoder function network. For example:

nss.Decoder = dlnet;

where dlnet is a custom dlnetwork object with one input representing the latent state and one output representing the original state.

For more information on autoencoders, see What are Neural State-Space Models?

Dimension of the internal (latent) state, specified as NaN or a positive integer. To add an encoder or decoder to your model, specify LatentDim as a positive integer.

Example: 2

Flag indicating time invariance, returned as one of the following:

This property is read-only and cannot be set using dot notation. You can only specify this properly when you create nss. To do so, use the corresponding name-value pair argument in idNeuralStateSpace. For example:

nss = idNeuralStateSpace(3,NumInputs=2,IsTimeInvariant=false)

Flag indicating direct feedthrough in the output networks, returned as false or as an array logical values.

If NumOutputs = nx, FeedthroughInOutputNetwork is false, because the only output is the measured state, and there is no contribution from any input.

If NumOutputs > nx, FeedthroughInOutputNetwork is a 1-by-2 logical array in which the elements are as follows.

Example: [false, false]

State names, specified as one of these values:

You can specify StateName using a string, such as "velocity", but the state name is stored as a character vector, 'velocity'.

Example: {'velocity','distance'}

State units, specified as:

Use StateUnit to keep track of the units each state is expressed in. StateUnit has no effect on system behavior.

If you specify StateUnit using a string, such as "mph", the state units are stored as a character vector, 'mph'.

Example: 'mph'

Example: {'rpm','rad/s'}

Independent variable name, specified as a string or character vector, for the state, input and output functions.

Example: "t"

Innovation covariance matrix, specified as an NumOutputs-by-NumOutputs positive semi-definite matrix. Typically this property is automatically set by the estimation algorithm.

Example: 1e-3*eye(2)

Names of input channels, specified as:

You can use automatic vector expansion to assign input names for multi-input models. For example, if sys is a two-input model, you can specify InputName as follows.

sys.InputName = 'controls';

The input names automatically expand to {'controls(1)';'controls(2)'}.

You can use the shorthand notation u to refer to the InputName property. For example, sys.u is equivalent to sys.InputName.

Input channel names have several uses, including:

If you specify InputName using a string or string array, such as "voltage", the input name is stored as a character vector, 'voltage'.

When you estimate a model using an iddata object, data, the software automatically sets InputName to data.InputName.

Units of input signals, specified as:

Use InputUnit to keep track of the units each input signal is expressed in. InputUnit has no effect on system behavior.

If you specify InputUnit using a string, such as "voltage", the input units are stored as a character vector, 'voltage'.

Example: 'voltage'

Example: {'voltage','rpm'}

Input channel groups, specified as a structure where the fields are the group names and the values are the indices of the input channels belonging to the corresponding group. When you use InputGroup to assign the input channels of MIMO systems to groups, you can refer to each group by name when you need to access it. For example, suppose you have a five-input model sys, where the first three inputs are control inputs and the remaining two inputs represent noise. Assign the control and noise inputs of sys to separate groups.

sys.InputGroup.controls = [1:3];sys.InputGroup.noise = [4 5];

Use the group name to extract the subsystem from the control inputs to all outputs.

sys(:,'controls')

Example: struct('controls',[1:3],'noise',[4 5])

Names of output channels, specified as:

You can use automatic vector expansion to assign output names for multi-output models. For example, if sys is a two-output model, you can specify OutputName as follows.

sys.OutputName = 'measurements';

The output names automatically expand to {'measurements(1)';'measurements(2)'}.

You can use the shorthand notation y to refer to the OutputName property. For example, sys.y is equivalent to sys.OutputName.

Output channel names have several uses, including:

If you specify OutputName using a string, such as "rpm", the output name is stored as a character vector, 'rpm'.

When you estimate a model using an iddata object, data, the software automatically sets OutputName to data.OutputName.

Units of output signals, specified as:

Use OutputUnit to keep track of the units each output signal is expressed in. OutputUnit has no effect on system behavior.

If you specify OutputUnit using a string, such as "voltage", the output units are stored as a character vector, 'voltage'.

Example: 'voltage'

Example: {'voltage','rpm'}

Output channel groups, specified as a structure where the fields are the group names and the values are the indices of the output channels belonging to the corresponding group. When you use OutputGroup to assign the output channels of MIMO systems to groups, you can refer to each group by name when you need to access it. For example, suppose you have a four-output model sys, where the second output is a temperature, and the rest are state measurements. Assign these outputs to separate groups.

sys.OutputGroup.temperature = [2];sys.OutputGroup.measurements = [1 3 4];

Use the group name to extract the subsystem from all inputs to the measurement outputs.

sys('measurements',:)

Example: struct('temperature',[2],'measurement',[1 3 4])

Text notes about the model, specified as a string or character vector. The property stores whichever of these two data types you provide. For instance, suppose that sys1 and sys2 are dynamic system models. You can set their Notes properties to a string and a character vector, respectively.

sys1.Notes = "sys1 has a string.";sys2.Notes = 'sys2 has a character vector.';sys1.Notessys2.Notes

ans = "sys1 has a string."ans = 'sys2 has a character vector.'

You can also specify Notes as string array or a cell array of character vectors or strings.

Sample time, specified as a nonnegative scalar, in units specified by the TimeUnit property. For a continuous time model, Ts is equal to 0 (default). Changing the value of Ts has no impact on the system data and does not discretize or resample the model.

Example: 0.1

Model time units, specified as:

If you specify TimeUnit using a string, such as "hours", the time units are stored as a character vector, 'hours'.

Model properties such as sample time Ts, InputDelay, OutputDelay, and other time delays are expressed in the units specified by TimeUnit. Changing this property has no effect on other properties, and therefore changes the overall system behavior. Use chgTimeUnit to convert between time units without modifying system behavior.

This property is read-only.

Summary report that contains information about the estimation options and results for a state-space model obtained using estimation commands. Use Report to find estimation information for the identified model, including the:

For more information on this property and how to use it, see the Output Arguments section of the corresponding estimation command reference page and Estimation Report.