Semi-Parametric Methods for Nonlinear System Identification

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The general research area covered in this proposal is System Identification of Structured Nonlinear Systems.This research is motivated by the fact that identification of complex nonlinear systems is of widespread importance in the engineering community for control, prediction, design, and diagnostics. The range of engineering applications include chemical processing, semiconductor manufacturing, automotive and aerospace applications, and bio-engineering.The broad objectives of research are to develop novel algorithms for the identification of complex nonlinear systems that respect a priori information regarding the structure of the interconnection, and that exploit the unprecedented computational power available today.It is anticipated that the proposed research will have broad impact in modeling, prediction and control for complex nonlinear processes. For example, the identification tools we intend to develop will make possible the development and verification of structural models. Also, these tools will allow for the efficient identification of interconnected nonlinear systems of higher complexity than previously possible. This, in turn, will enable high-performance control system design for such systems. Additionally, our research will spawn numerical tools for nonlinear structured model reduction.Specific research topics that are addressed in this proposal include:(1) the development of novel system identification algorithms for interconnected nonlinear systems, (2) the analysis of these algorithms from the context of convergence, efficiency, and optimality, (3) the design of numerically stable, computationally attractive implementations of these algorithms, (4) the study of closely related issues in this context such as optimal experiment design, identifiability, undermodeling and noise effects on estimation accuracy, and finite-sample algorithm behavior, (5) a theoretical investigation of the fundamental limitations on the accuracy to within which it is possible to identify components in an interconnected modelA wide variety of techniques will be used. These include optimization, nonlinear programming, computational geometry, operator theory, numerical linear algebra, and probability theory.