Semi-Parametric Methods for Nonlinear System Identification

本论文的主要研究领域是结构化非线性系统的系统辨识，其研究动机是复杂非线性系统的辨识在工程界的控制、预测、设计和诊断中具有广泛的重要性。 工程应用的范围包括化学加工，半导体制造，汽车和航空航天应用，以及生物工程。研究的广泛目标是开发新的算法，用于识别复杂的非线性系统，尊重先验信息的结构的互连，并利用了当今前所未有的计算能力。预计拟议的研究将在建模方面产生广泛的影响，复杂非线性过程的预测和控制。 例如，我们打算开发的识别工具将使结构模型的开发和验证成为可能。 此外，这些工具将允许更高的复杂性比以前可能的相互关联的非线性系统的有效识别。 这反过来又将使高性能的控制系统设计这样的系统。 此外，我们的研究将催生非线性结构化模型简化的数值工具。本提案中涉及的具体研究主题包括：（1）开发用于互连非线性系统的新颖系统辨识算法，（2）从收敛性、效率和最优性的背景分析这些算法，（3）设计这些算法的数值稳定的、计算上有吸引力的实现，（4）研究在此背景下密切相关的问题，例如最优实验设计、可辨识性、欠建模和噪声对估计精度的影响，和有限样本算法的行为，（5）对在互连模型中识别组件的精度的基本限制的理论研究将使用各种各样的技术。这些课程包括最优化、非线性规划、计算几何、算子理论、数值线性代数和概率论。

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.