Indentification of nonlinear systems using canonical variance analysis

A new approach to the identification of nonlinear systems is developed based upon state affine (SA) models of nonlinear systems, canonical variate analysis (CVA) for optimal selection of the affine state, estimation of the state affine model parameters by regression, and determination of model state order and structure using the Akaike information criterion (AIC). For processes where the conditional expectation of the output given the past is a continuous function of the past, affine Markov processes are shown to provide approximations of arbitrary accuracy. An innovation representation gives directly the optimal nonlinear filter for affine Markov process. CVA gives an optimal selection of the affine state as linear combinations of polynomials in the past inputs and outputs. CVA computations involve primarily a singular value decomposition which is numerically stable and accurate. Given the CVA state, the coefficients of state affine models are fitted by simple polynomial regression procedures. Selection of the state order and model structure is made using the AIC.