Identification of nonlinear systems using a B-splines parametric subspace approach

System identification theory has benefited from developments in numerical linear algebra, in particular, generalizations and extensions of the singular value decomposition. Thanks to these new developments, a new class of algorithms collectively known as subspace algorithms has emerged. These algorithms have the advantage of working directly in the state-space domain, which makes them quite appealing for designing model-based controllers. Extensions to nonlinear systems have appeared for bilinear and Hammerstein systems. We introduce a B-splines subspace approach for identifying nonlinear systems. It is based on a parametric B-splines transformation of the inputs, followed by linear system identification. In this sense, our approach identifies a Hammerstein model with B-splines as the input basis. Since the inputs depend parametrically on the spline functions, an iterative procedure is developed for obtaining the optimal parameters. An example of a rainfall-runoff application is presented.