NONLINEAR STRUCTURE IDENTIFICATION :
This paper investigates new ways of inferring nonlinear dependence parsimoniously from measured data. The existence of unique linear and nonlinear sub-spaces which are structural invariants of general nonlinear maps is established for the first time. Necessary and sufficient conditions determining these sub-spaces are derived. In addition to being of considerable interest in their own right, 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 subspaces 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.