An alternating optimization method for switched linear systems identification

The identification of switched systems involves solving a mixed-integer optimization problem to determine the parameters of each mode dynamics (continuous part) and assign the data to the modes (discrete part), so as to minimize a cost criterion measuring the quality of the model on a set of input/output data collected from the system. Oftentimes, some a priori information on the switching mechanism is available, e.g., in the form of a minimum dwell time. This information can be encoded in a suitable constraint and included in the optimization problem, but this introduces a coupling between the discrete and continuous optimization variables that makes the problem harder to solve. In this paper, we propose an iterative approach to the identification of switched systems that alternates a minimization step with respect to the continuous parameters of the modes, and a minimization step with respect to the discrete variables defining the data-modes mapping. Constraints originating from {a priori} knowledge on the switching mechanism are enforced after the (unconstrained) discrete optimization step through a post-processing phase. These three phases are repeated until a stopping criterion is met. A comparative numerical analysis of the proposed method shows its improved performance with respect to competitive approaches in the literature.