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1 2010

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Optimal pre-correction with the use of pseudo-inverse maps as the result of modeling and optimal past-correction from the functional theory of nonlinear systems perspective

Ciesielski G., Sobańska P.

Systems Science

2010

Vol. 36, no 4

59-69

This paper presents a new idea of pseudo-inverse maps applied to the optimal pre-corrections of nonlinear systems. This notion is the result of search for optimal models and optimal past-correctors of nonlinear systems from the perspective of the Functional Theory of Nonlinear Systems discussed in this article. The systems considered are multidimensional, which means that they have any finite number of inputs and outputs. The signals on inputs and outputs are real or complex valued. Furthermore, the input and output signal sets are finally equipped with the structure of the Hilbert spaces. The maps considered are functions for the static systems, convolutions for the linear time-invariant systems and nonlinear operators for the nonlinear systems. It is worth noting that the nonlinear systems past- and pre-corrections presented in this paper are reduced to the modeling tasks of some systems which, in turn, can be reduced further to the generalized least mean square (LMS) approximations.