Semi-Parametric Methods for Nonlinear System Identification

本提案所涵盖的一般研究领域是结构化非线性系统的系统辨识。复杂非线性系统的识别在工程社区的控制、预测、设计和诊断中具有广泛的重要性，这一事实促使了本研究的开展。工程应用范围包括化学加工、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来识别复杂的非线性系统，这些系统尊重有关互连结构的先验信息，并利用当今前所未有的计算能力。预计本文的研究将在复杂非线性过程的建模、预测和控制方面产生广泛的影响。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，这些工具将允许比以前更复杂的互连非线性系统的有效识别。反过来，这将使此类系统的高性能控制系统设计成为可能。此外，我们的研究将产生非线性结构模型简化的数值工具。本提案所涉及的具体研究课题包括：(1)开发用于互联非线性系统的新型系统识别算法，(2)从收敛、效率和最优性的角度分析这些算法，(3)设计这些算法在数值上稳定、计算上有吸引力的实现，(4)在此背景下研究密切相关的问题，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，以及有限样本算法行为，(5)对准确度基本限制的理论研究，在这种限制内，可以识别相互关联模型中的组件。将使用各种各样的技术。这些包括最优化、非线性规划、计算几何、算符理论、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.