Identification of nonlinear parameter-varying systems via canonical variate analysis

This paper gives a tutorial presentation of the canonical variate analysis (CVA) method of subspace system identification for linear time- invariant (LTI), linear parameter-varying (LPV), and nonlinear parameter-varying (NLPV) systems. The paper takes a first principles statistical approach to rank determination of deterministic vectors usinig a singular value decomposition (SVD), followed by a statistical multivariate CVA as rank constrained regression. This is generalized to LTI dynamic systems, and extended directly to LPV and NLPV. The computational structure and problem size is very similar to LTI subspace methods except that the matrix row dimension (number of lagged variables of the past) is multiplied by the effective number of parameter-varying functions. This is in contrast with the exponential explosion in the number of variables using current subspace methods for LPV systems. Compared with current methods, initial results indicate much less computation, maximum likelihood accuracy, and better numerical stability. The method applies to systems with feedback, and can automatically remove a number of redundancies in the nonlinear models producing near minimal state orders and polynomial degrees by hypothesis testing. There is detailed discussion of the methods and structure of the computational modules.