Nonlinear Time-varying Systems Identification by Fuzzy Linear Programming Support Vector Regression

Abstract

Nonlinear black-box system identification is the process of deducing a mathematical model of the internal dynamics of a nonlinear system from observations of its outputs, which represents the relationship between past input-output data and present/future outputs of the system, when very little priori knowledge is available. As a new generation of learning algorithms, support vector regression (SVR) was developed by Vapnik et.al recently, in which e-insensitive loss function was defined as a trade-off between the robust loss function of Huber and one that enables sparsity within the SVs. The use of support vector kernel expansion also provides us a potential avenue to represent nonlinear dynamical systems and underpin advanced analysis. However, in the support vector regression with the standard quadratic programming technique, its implementation is more computationally expensive and sufficient model sparsity can not be guaranteed. In this article, particular attention is paid to the sparsity of the generated model and the model tracing ability for time-varying nonlinear systems and fuzzy linear programming support vector regression (LP-SVR) was proposed for identifying time-varying nonlinear dynamical systems identification.