Canonical variate analysis in identification, filtering, and adaptive control

The canonical variate analysis (CVA) approach for system identification, filtering, and adaptive control is developed. The past/future Markov property provides a starting point for defining a reduced-order prediction problem. The solution is a canonical variate analysis that is characterized by a generalized singular value decomposition. State-space model estimation requires only simple regression, and state order selection involves the optimal Akaike information criterion procedure. The CVA method extends to time-varying and abruptly changing systems. A reduce-rank stochastic model predictive control problem is shown to be equivalent to the CVA problem. Also discussed are computational aspects, applications, and an example illustrating the method. New extensions to the identification of general nonlinear systems are briefly discussed. The CVA method provides an approach giving reliable, automatic implementation of identification, filtering, and control for online adaptive control