System identification for structured nonlinear systems

This dissertation deals with various aspects of identification problems for structured nonlinear systems. Structure arises from prior knowledge of the interconnections in the physical system being identified. We assume no further a priori information, such as basis expansion of nonlinear maps or the knowledge of the state dimension of linear subsystems. This naturally leads us to investigate non-parametric approaches. These non-parametric identification problems commonly occur in process control applications and in nonlinear model reduction problems.; While many problems in linear system identification have been addressed, their nonlinear counterparts remain largely unexplored. Many physical systems exhibit significant nonlinear behavior, which is often approximated by linear models for the purpose of identification, prediction, and control. With the increasing demand for better performance and higher fidelity, techniques for nonlinear system identification must be developed.; In this thesis, we first establish a general paradigm for nonlinear structured models based on linear fractional transformations (LFTs). Essentially, this paradigm involves decomposing the model into linear dynamic and static nonlinear components. These components inherit structure from prior information about the system being identified. Any nonlinear model can be cast into this format. Our two principle contributions are the analysis of identifiability and the development and analysis of novel identification algorithms for this model structure.; Loosely speaking, a model is identifiable if the unknown components can be determined uniquely using input-output experiments. Identifiability concepts are of fundamental importance in system identification. Here, we investigate identifiability for nonlinear structured models using the general LFT paradigm.; In using the general LFT paradigm for identification, the linear dynamic and static nonlinear components have to be resolved from experimental data. For this we need a general cost function that captures deviation from static nonlinear behavior. This development and the consequent analysis of identification algorithms constitutes the second focus of this dissertation.