Application Gravitational Search Algorithm in Identification of Switched Linear Systems

The work presented in this paper is concerned with the identification of switched linear systems from input-output data. The main challenge with this problem is that the data are available only as a mixture of observations generated by a finite set of different interacting linear subsystems so that one does not know a priori which subsystem has generated which data. To overcome this difficulty, we formally pose the problem of identifying each submodel as a combinatorial ℓ₀ optimization problem. To decrease the complexity of this NP-hard problem we use a gravitational search algorithm, we present sufficient conditions for this relaxation to be exact. The whole identification procedure allows us to extract the parameter vectors (associated with the different subsystems) one after another without any prior clustering of the data according to their respective generating submodels. Some simulation results are included to support the potentialities of the proposed method.