CVA identification of nonlinear systems with LPV state-space models of affine dependence

This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial shifted form based LPV Autoregressive with eXogenous input (ARX) model to the observed input-output data. The estimated ARX model is used for filtering away the effects of future inputs on future outputs to obtain the so called “corrected future” analogous to the LTI case. The generality of the applied LPV-ARX parametrization now permits the estimation of the input-output map of a rather general class of LPV state-space models with matrices depending affinely on the scheduling. This is achieved by a canonical variate analysis (CVA) between the past and the corrected future which provides an estimate of a relevant set of state variables and their trajectories for the system, necessary for the construction of the minimal order state equations.