Neural State-Space Models

Use neural networks to represent the functions defining the nonlinear state space realization of your system

Neural state-space models are a type of nonlinear state-space models where the state-transition and measurement functions are modeled using neural networks. You can identify the weights and biases of these networks using System Identification Toolbox™ software. You can use the trained model for control, estimation, optimization, and reduced order modeling.

Live Editor Tasks

Estimate Neural State-Space Model

Estimate neural state-space model in the Live Editor (Since R2023b)

Functions

`createMLPNetwork`	Create and initialize a Multi-Layer Perceptron (MLP) network to be used within a neural state-space system (Since R2022b)
`setNetwork`	Assign `dlnetwork` object as the state or output function of a neural state-space model (Since R2024b)
`nssTrainingOptions`	Create training options object for neural state-space systems (Since R2022b)
`nlssest`	Estimate nonlinear state-space model using measured time-domain system data (Since R2022b)
`generateMATLABFunction`	Generate MATLAB functions that evaluate the state and output functions, and their Jacobians, of a nonlinear grey-box or neural state-space model (Since R2022b)
`idNeuralStateSpace/evaluate`	Evaluate a neural state-space system for a given set of state and input values and return state derivative (or next state) and output values (Since R2022b)
`idNeuralStateSpace/linearize`	Linearize a neural state-space model around an operating point (Since R2022b)
`sim`	Simulate response of identified model

Objects

`idNeuralStateSpace`	Neural state-space model with identifiable network weights (Since R2022b)
`nssTrainingADAM`	Adam training options object for neural state-space systems (Since R2022b)
`nssTrainingSGDM`	SGDM training options object for neural state-space systems (Since R2022b)
`nssTrainingRMSProp`	RMSProp training options object for neural state-space systems (Since R2024b)
`nssTrainingLBFGS`	L-BFGS training options object for neural state-space systems (Since R2024b)

Blocks

Neural State-Space Model

Simulate neural state-space model in Simulink (Since R2022b)

Topics

What are Neural State-Space Models?
Understand the structure of a neural state-space model.
Neural State-Space Model of SI Engine Torque Dynamics
This example describes reduced order modeling (ROM) of the nonlinear torque dynamics of a spark-ignition (SI) engine using a neural state-space model.
Neural State-Space Model of Simple Pendulum System
This example shows how to design and train a deep neural network that approximates a nonlinear state-space system in continuous time.
Augment Known Linear Model with Flexible Nonlinear Functions
This example demonstrates a method to improve the normalized root mean-squared error (NRMSE) fit score of an existing state-space model using a neural state-space model.
Reduced Order Modeling of a Nonlinear Dynamical System using Neural State-Space Model with Autoencoder
This example shows reduced order modeling of a nonlinear dynamical system using a neural state-space (NSS) modeling technique.
Reduced Order Modeling of Electric Vehicle Battery System Using Neural State-Space Model
This example shows a reduced order modeling (ROM) workflow, where you use deep learning to obtain a low-order nonlinear state-space model that serves as a surrogate for a high-fidelity battery model.