Practical Methods for the Identification of Nonlinear Systems

系统识别指的是一类数据驱动的技术，它通过测量动态系统的输入和输出来构建动态系统的数学模型。系统识别与机器学习和人工智能密切相关，是高性能控制系统设计、自动故障检测方法和动态系统定量研究背后的使能技术。最初的工作集中在线性时不变系统的识别上，并且已经产生了一种成熟的技术，记录在许多教科书中，并得到了一些商业工具的支持。另一方面，非线性和/或时变系统的辨识仍然是一个活跃的研究领域，其应用在很大程度上仍然局限于该领域的专家。所提出的研究计划的长期目标是缩小非线性系统辨识方法的理论发展与实际应用之间的差距。特别是，我们将创建非专业人员可以使用的方法，这些方法可以使用在典型实验条件下收集的数据来识别具有实际意义的广泛系统。为了实现这一目标，我的团队将追求两个互补的研究方向：第一个研究主题将开发识别在反馈控制回路内运行的非线性系统的方法。在控制工程环境中，出于经济或安全原因，通常需要闭环操作。反馈回路的存在增加了识别的复杂性，因为由于反馈回路，输出测量中的误差最终会出现在系统的输入中。因此，在这种情况下，干扰与系统输入无关的假设被打破了。虽然线性系统的闭环辨识方法已经得到了广泛的发展，但将其推广到非线性系统仍然是一个悬而未决的问题。第二个主要主题涉及开发鲁棒的“交钥匙”方法来识别非线性状态空间（NLSS）系统。这类系统已被证明比可以用Volterra级数表示的系统更广泛，因为它包括线性化后的系统，其极点随着系统工作点的变化而移动。NLSS模型也可以表示任何Volterra系统，也可以表示具有移动极点的系统。我的团队将开发识别这些系统的方法，这些方法可以在最少的用户输入下使用。最后，将这两个主题合并，并扩展NLSS识别方法，使其能够使用闭环收集的数据。在闭环中识别非线性系统动力学的能力将对各种控制应用产生重大影响，因为它消除了对专用模型校准实验的需要，从而降低了与控制系统设计相关的成本。

System identification refers to a class of data-driven techniques that construct mathematical models of dynamic systems from measurements of their input(s) and output(s).  Closely related to machine learning and artificial intelligence, system identification is the enabling technology behind the design of high-performance control systems, automatic fault detection methods and the quantitative study of dynamic systems.  Initial work focused on the identification of linear, time-invariant systems, and has produced a mature technology documented in numerous textbooks and supported by several commercially available tools. The identification of nonlinear and/or time-varying systems, on the other hand, is still an active research field whose application is still largely restricted to specialists in the field. The long-term goal of the proposed research program is to close the gap between the theoretical development and practical application of nonlinear system identification methods. In particular, we will create methods that can be used by nonspecialists that can identify a broad class of systems that are of practical interest using data gathered under typical experimental conditions. In moving toward this objective, my team will pursue two complimentary lines of research: The first research theme will develop methods for the identification of nonlinear systems that are operating inside of feedback control loops. In a control engineering context, closed-loop operation is often required either for economic or safety reasons. The presence of a feedback loop adds complexity to the identification, as errors in the output measurement eventually appear in the system's input, due to the feedback loop. Thus, the assumption that the disturbances are independent of the system input breaks down in this case. While solutions for closed-loop identification of linear systems have been extensively developed, their extension to nonlinear systems remains an open problem. The second major theme involves developing robust, "turn-key" methods for the identification of nonlinear state-space (NLSS) systems. This class of systems has been shown to be much broader that the class of systems that can be represented by a Volterra series, in that it includes systems, when linearized, whose poles move with changes in the system's operating point. NLSS models, which can also represent any Volterra system, can also represent systems with moving poles. My team will develop methods for the identification of these systems, that can be used with a minimum of user input. Finally, the two themes will be merged, and the methods for NLSS identification will be extended to enable the use of data gathered in closed-loop. The ability to identify nonlinear system dynamics in closed loop will have a significant impact in a variety control applications by eliminating the need for dedicated model calibration experiments thus reducing the cost associated with control system design.