| This dissertation is concerned with the identification of interconnected nonlinear systems. Specifically, we focus on systems composed of linear dynamical components and static nonlinear maps.;The study of nonlinear system identification is still in its early stages, and thus tackling the most general problems should not be an immediate goal. We can find great value in studying particular classes of systems to obtain computationally tractable algorithms and insightful theoretical results. This, together with past work and experimental studies, will provide us with the necessary analytical and computational tools to better understand the large variety of practical identification problems that we encounter today.;We make use of the linear fractional transformation framework to capture all interconnected nonlinear systems into a single unified setting. This allows us to study various aspects of system identification problems such as algorithms, identifiability, persistence of excitation, experiment design, and convergence, from the same perspective for a large class of systems. Results pertaining to subclasses of the systems that we consider can then be recovered as special cases of this general treatment.;In our formulation, we make two key assumptions: the linear components of the interconnection are known, and the inputs to all the nonlinear functions are measurable. Even under these restrictions, the class of systems we consider is rich and encompasses many practical problems of interest. Moreover, we argue that measurability of the inputs to the nonlinear functions is a key ingredient towards the computational tractability of any nonlinear system identification algorithm. Under these assumptions, we propose an identification algorithm that systematically incorporates a priori interconnection information and enforces the requirement that the nonlinearities represent static mappings. Our estimates are offered nonparametrically so that no prejudices are incurred as the result of artificial parameterizations, and it is shown that this algorithm reduces to a linear least squares problem.;The estimated nonlinearities are proven to converge to their true values under certain conditions. A critical requirement for convergence is one that subsumes the standard notions of identifiability and persistence of excitation. We provide sufficient conditions and computational tests to illuminate these prerequisites for convergence. |
