Reading Ljung.  System Identification: theory for the user.

1: Introduction.

Goal: infer a model from observations.  “Model” refers to the set of relationships between variables in the system.  System identification involves analyzing input and output signals from the system.

Example: assume a linear difference equation relates inputs to outputs.  Use least squares to find parameter values that minimize the least squares error.  This is partly an autoregression: a linear regression “where the regression vector contains old values of the variable to be explained”.

Adding noise: assume the observed data are from a deterministic process with noise.  We’re interested in two expectation values: the parameters and the covariance of the parameter error.

System identification involves: a data set, candidate models, and an assessment rule (see chapter 7).  Then use model validation to check whether the model is good enough.  This process ends up being iterative.

2: Time invariant linear systems.

Impulse response can be used to characterize the system.  If there’s an additive disturbance info is needed on that too (spectrum and pf).

3: Simulation and prediction.

4: Models of linear time-invariant systems.

5: Models for time-varying and nonlinear systems.

Linear time-varying models might be used when we linearize a nonlinear system about some trajectory.

6: Nonparametric time and frequency domain methods.

7: Parameter estimation methods.

8: Convergence and consistency.

9: Asymptotic distribution of parameter estimates.

10: Computing the estimate.

11: Recursive estimation methods.

12: Options and objectives.

 

13: Experiment Design.

14: Preprocessing data.

15: Choice of identification criterion.

16: Model structure selection and model validation.

17: System identification in practice.