# Nonlinear system identification with known model

I would like to ask for suggestions regarding system identification with known model structure, but without known parameters.

The model is a model of a physical system, it can be assumed that it is stable, non-linear and dynamic. The input/output data are available with and without noise.

While the model structure is known, the values of the parameters are unknown. The models have up to 10 parameters (just to give you a hint about dimensionality).

Options I am aware of to solve these problems:

1. quasi-random search algorithms (Particle Swarm, Genetic Algorithm, ...)
2. gradient based methods (backpropagation through time, forward perturbation, ...)

QUESTION:

What other techniques are there to solve this kind of problems ?

• Under identifying I would understand that you look at the data and then e.g. get an idea this is a solution of the nonlinear Foo-Bar equation. As you write "with known model structure" I assume you have this part tackled and are now trying to squeeze the $42$ parameters which show up in the Foo-Bar equation out of your data? – mvw Aug 9 '18 at 10:07
• @mvw Yes, the parameters have physical meaning. Also I am not working with hyper-parametrized model. Therefore I need to "tune" relatively low number of parameters to match my measured data. – Martin G Aug 9 '18 at 10:25
• I have used Evolutionary Strategies (ES-CMA) in problems of parametric identification in differential equations, with notable success. – Cesareo Aug 9 '18 at 10:35
• @Cesareo Thank you, in my understanding, "evolutionary strategies" are the quasi-random search algorithms. From my experience they are very computational power hungry, which makes them not suitable for low-power embedded devices. Maybe I can clarify, the EA itself is simple, it is the evaluation of individual/particles/genes that requires a lot of computational power (e.g. simulation of nonlinear system, etc) – Martin G Aug 11 '18 at 11:45
• @MartinG Why do not we do a test? I use a completely normal personal computer in my calculations. Propose an example and we will try to solve it using various techniques. – Cesareo Aug 11 '18 at 12:17