Identification of Switched Linear System Based on Dynamic Programming

In this work, a new algorithm based on dynamic programming is presented for the identification of the switched linear system which consists of a finite number of linear subsystems activated by a switched mechanism. The identification problem is essentially a mixed-integer programming problem and includes the estimation of the parameters for each submodel as well as the determination of switching instants. In this paper, a new identification algorithm for switched linear systems based on dynamic programming is proposed. By using dynamic programming, the submodel parameters and the switching instants can be estimated in a global way, and further a criterion is used to select the number of the segments. Under some necessary assumptions, the dynamic programming can be solved with the polynomial-time complexity. Based on K-means clustering, all different segmented data belonging to the same mode can be concatenated and used to identify the final mode parameters and the elbow method is applied to identify the number of the submodels. Numerical experiments are given to demonstrate the effectiveness of the proposed identification method.