A Two-stage Identification Method for Switched Linear Systems

Abstract: In this work, a new two-stage identification method based on dynamic programming and sparsity inducing is proposed for switched linear systems. Our method achieves sparsity inducing in the identification of switched linear systems by the constrained switching mechanism, in contrast to previous optimization-based identification techniques that rely on the rigid data distribution assumption in the parameter space. The proposed mechanism assumes the existence of a minimal interval between adjacent switching instants. First, an efficient iterative dynamic programming approach is used to determine the switching instants and segments using the constrained switching mechanism. Then, each submodel is identified as a combinatorial $\ell_0$ optimization problem, and the true parameter for each submodel is determined by solving the problem. The problem of combinatorial $\ell_0$ optimization is solved by relaxing it into a convex $\ell_1$-norm optimization problem. Furthermore, the unbiasedness of the switched linear system identification is discussed thoroughly with the constrained switching mechanism and a new persistent excitation condition is proposed. Simulation experiments are conducted to indicate that our algorithms exhibit strong robustness against noise.