A Rank Minimization Formulation for Identification of Linear Parameter Varying Models⁎. Issue 26 (2018) - Singh, Rajiv; Sznaier, Mario; Ljung, Lennart
Abstract: We explore the problem of identification of LPV models when the scheduling variables are not known in advance and the model parameters exhibit a dynamic dependence on them. We consider an affine ARX model structure whose parameters vary with time. We solve for the model's parameters and scheduling variables in two steps. In the first step, we use the measured input-output data to realize a parameter trajectory by solving a regularized Hankel matrix rank minimization problem. The regularization penalty is guided by the prior knowledge regarding the nature of system's time variation. In the second step, the scheduling variables are estimated as parameters of a sparse ARX structure relating the model's parameters to the measured input-output variables. The effectiveness of the proposed approach is illustrated with two practical examples.