Experiment design for continuous-time systems using generalized filtering
Jiwei Wang, Simone Baldi, Henk J. van Waarde
TL;DR
The paper develops a generalized filtering framework to enable experiment design for continuous-time systems when derivatives of trajectories are not measured. By linking filtered data to sampled data and establishing rank-based informativity conditions, it shows how to design inputs online to guarantee identifiability with the minimal number of samples ($M=n+m$). The method is demonstrated on aircraft longitudinal dynamics, where filtered-sampled data achieve full rank and yield highly accurate reconstructions of the system matrices. This approach provides a sample-efficient, derivative-free path for data-driven identification and control of continuous-time systems. The results bridge continuous-time Willems-type fundamentals with practical online input design and broad filtering possibilities.
Abstract
The goal of experiment design is to select the inputs of a dynamical system in such a way that the resulting data contain sufficient information for data-driven modeling and control. This paper investigates the problem of experiment design for continuous-time systems under piecewise constant input signals. To obviate the need for measuring time derivatives of (data) trajectories, we introduce a generalized filtering framework. Our main result is to establish conditions on the input and the filter functions under which the filtered data are informative for system identification, i.e., they satisfy a certain rank condition. The proposed framework encompasses several filter functions that have already appeared in the literature. Building on the proposed filtering framework, we develop an experiment design procedure where the input signal is designed online during system operation. This method is shown to be sample efficient, in the sense that it deals with the least possible number of filtered data samples for system identification.