Summary

Abstract

The principal focus of this book has been on the topic of discrete-time Volterra models, motivated first by the need for discrete-time dynamic models as a basis for nonlinear model-based computer control applications, and second by the analytical and practical advantages of the Volterra model class relative to other nonlinear model classes. In particular, the class of discrete-time Volterra models may be viewed as a generically well-behaved extension of the class of linear FIR models on which typical linear MPC applications are based. One general feature of finite Volterra models discussed in Chapter 2 is that these models preserve many important qualitative characteristics of the input sequence, including boundedness (i.e. all V(_N,_M) models are BIBO stable), asymptotic constancy, and periodicity. These observations stand in marked contrast to even the simplest of polynomial models involving nonlinear autoregressive terms, which generally exhibit more strongly nonlinear behavior, including nonperiodic responses to periodic inputs, input-dependent stability, and responses to asymptotically constant inputs that do not settle out to constant values (e.g. chaotic step responses). In addition, since stable linear models that include autoregressive terms also preserve these input characteristics, many of the generic characteristics of the V(N,M) model class carry over to extensions like the AR-Volterra model class, which include linear autoregressive terms.