Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
This work addresses the need for efficient and accurate system identification across various dynamical models, offering a practical improvement over slower state-of-the-art methods, though it is incremental in its approach.
The authors tackled the problem of identifying a broad range of dynamical systems, including linear, parameter-varying, and nonlinear models with noise, by developing a general system identification procedure that uses neural networks and efficient optimization. They achieved training times in seconds, compared to hours for existing methods, and demonstrated superior accuracy and computational efficiency on benchmark problems.
We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.