Volterra and Wiener Model Based Temporally and Spatio-Temporally Coupled Nonlinear System Identification: A Synthesized Review

Abstract

Nonlinear problems have drawn the attention of many researchers, engineers and scientists as most of the real systems are inherently nonlinear in nature. These systems widely exist in many industrial processes such as thermal process, fluid process, pH neutralization process, and so on. They can be customarily classified into lumped parameter systems (LPSs) and distributed parameter systems (DPSs). Modeling of these systems is quite arduous, but is essential for prediction, control, and analysis. To model and analyze these nonlinear systems, many theoretical and practical methods including Volterra and block-structured models have been developed. The main objective of this paper is to concisely present the Volterra and block-structured modeling approaches along with their vital applications to nonlinear system identification and control. A much-needed effort is given in describing various modeling methods for unknown DPSs. As DPSs are of infinite dimensionality, hence they require model reduction (MR) techniques for practical implementation. Various types of MR techniques are studied in this paper where the efficient selection of spatial basis-functions is often required. Further, the adaptive modeling methods for LPSs and DPSs are studied to inculcate the benefits of adaptiveness. Finally, wireless sensor network-based distributed consensus modeling of nonlinear DPSs is discussed, diminishing the limitations of least-squares and centralized adaptive methods.