Method of Hybrid Approximations for Modelling of Multidimensional Nonlinear Systems

Authors:
Anatoli Torokhti;Phil Howlett;Charles Pearce
Affiliations:
Centre for Industrial and Applicable Mathematics, University of South Australia, SA 5095, Australia anatoli.torokhti@unisa.edu.au;Centre for Industrial and Applicable Mathematics, University of South Australia, SA 5095, Australia phil.howlett@unisa.edu.au;Applied Mathematics Department, University of Adelaide, SA 5001, Australia cpearce@maths.adelaide.edu.au
Venue:
Multidimensional Systems and Signal Processing
Year:
2003

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Abstract

In this paper we propose a new approach to the constructive mathematical representation of nonlinear systems transforming stochastic signals. The approach is based on a combination of a new best approximation technique and a new iterative procedure. For each iteration, the approximation is constructed as a polynomial operator of degree r which minimizes the mean–squared error between a desired output signal and the output signal of the approximating system. We show that this hybrid technique produces a computationally efficient and flexible method for modelling of nonlinear systems. The method has two degrees of freedom, the degree r of the approximating operator and the number of iterations, to decrease the associated error.