Sparse Estimation for Predictor-Based Subspace Identification of LPV Systems

This paper presents a Basis Pursuit DeNoising (BPDN) sparse estimation approach as a regularization technique in a predictor-based subspace method for the identification of Linear ParameterVarying (LPV) state-space systems. It is known that in this identification method, the choice of the past window of a state predictor factorization will influence the conditioning of the main parameter estimation problem. Therefore, prior knowledge of the system order may be needed to choose the past window in such a way that this problem is well-conditioned. It will be demonstrated that sparse estimation through BPDN can reduce the sensitivity of the conditioning with respect to the past window parameter. In this way, we can simplify the task of choosing the past window to an extend that the need for prior knowledge of the system order is eliminated. Also, this paper will pay attention to the synthesis of stabilizing observer gain matrices in the identified LPV innovation-type state-space model.