System Identification Toolbox™

Supported Grey-Box Models

If you understand the physics of your system and can represent the system using ordinary differential or difference equations (ODEs) with unknown parameters, then you can use System Identification Toolbox commands to perform linear or nonlinear grey-box modeling. Grey-box model ODEs specify the mathematical structure of the model explicitly, including couplings between parameters and known parameter values. Grey-box modeling is useful when you know the relationships between variables, constraints on model behavior, or explicit equations representing system dynamics.

The toolbox supports both continuous-time and discrete-time models. However, because most laws of physics are expressed in continuous time, it is easier to construct models with physical insight in continuous time, rather than in discrete time.

In addition to dynamic input-output models, you can also create time-series models that have no inputs and static models that have no states.

If it is too difficult to describe your system using known physical laws, you can perform black-box modeling.

You can also use the idss model object to perform structured model estimation by using structure matrices As, Bs, Cs, Ds, X0s, Ks to fix or free specific parameters. However, you cannot use this approach to estimate arbitrary structures (arbitrary parameterization). For more information about structure matrices, see How to Estimate State-Space Models with Structured Parameterization.

ODE Parameter Estimation (Grey-Box Modeling)

Data Supported by Grey-Box Models