Practical Methods for the Identification of Nonlinear Systems

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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.