Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping

Leith, D.J. and Leithead, W.E. and Murray-Smith, R. (2006) Inference of disjoint linear and nonlinear sub-domains of a nonlinear mapping. Automatica, 42 (5). pp. 849-858. ISSN 0005-1098

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Abstract

This paper investigates new ways of inferring nonlinear dependence from measured data. The existence of unique linear and nonlinear sub-spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub-spaces are derived. The importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task. Specifically, once the linear/nonlinear sub-spaces are known, by definition the explanatory variables may be transformed to form two disjoint sub-sets spanning, respectively, the linear and nonlinear sub-spaces. The nonlinear modelling task is confined to the latter sub-set, which will typically have a smaller number of elements than the original set of explanatory variables. Constructive algorithms are proposed for inferring the linear and nonlinear sub-spaces from noisy data.