A randomized method for the identification of switched NARX systems

The identification of switched systems is a complex optimization problem that involves both continuous (parametrizations of the local models, a.k.a. modes) and discrete variables (model structures, switching signal). In particular, the combinatorial complexity associated with the estimation of the switching signal grows exponentially with the number of samples, which makes data segmentation (i.e. estimating the number and location of mode switchings, and the mode sequence) a challenging problem. In this work, we extend a previously developed randomized approach for the identification of switched systems to encompass the estimation of the switching locations. The method operates by extracting samples from a probability distribution of switched models, and gathering information from the associated model performances to update the distribution, until convergence to a limit distribution associated to a specific model. A suitable probability distribution is employed to represent the likelihood of a mode switching at a certain time, and the update process is designed to correct the switching locations and remove redundant switchings. The proposed algorithm has been compared to existing state-of-the-art methods and has been tested on various benchmark examples, to demonstrate its effectiveness.