Parameter estimation Grey-box modeling: Difference between 'lsqnonlin' / 'fmincon' / 'greyest'

Dear Community,

could anybody please explain me the difference between 'lsqnonlin' / 'fmincon' / 'greyest' in content with Parameter Estimation of Grey-Box models (RC-models)?

Thank you in advance.

Answer 1

[Udit06]

Hi Verena,

Each method uniquely addresses different modeling and optimization requirements.

greyest is designed for linear grey-box models with a known structure, making it highly effective for system identification by using input-output data to estimate parameters.

On the other hand, fmincon serves as a flexible nonlinear optimization tool, ideal for tackling problems with complex constraints by minimizing a scalar objective function within specified bounds.

In contrast, lsqnonlin is adept at handling nonlinear least-squares challenges, concentrating on reducing the sum of squared residuals, which makes it particularly well-suited for curve fitting tasks that do not involve extensive constraints.

You can refer to the following MathWorks documentations for more details:

• https://www.mathworks.com/help/optim/ug/lsqnonlin.html
• https://www.mathworks.com/help/ident/ref/greyest.html
• https://www.mathworks.com/help/optim/ug/fmincon.html

I hope this helps.