Online experiment design for continuous-time systems using generalized filtering

TL;DR

This paper presents a novel filtering-based approach for designing experiments in continuous-time systems with piecewise constant inputs, enabling efficient online data collection for system identification.

Contribution

It introduces a generalized filtering framework that avoids measuring derivatives and develops an online experiment design method for continuous-time systems.

Findings

The filtering framework ensures data informativeness for system identification.

The proposed method is sample efficient, using minimal filtered data samples.

It extends discrete-time experiment design techniques to continuous-time systems.

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 system identification and data-driven 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. We assume that the filter functions are piecewise continuously differentiable, encompassing several filter functions that have appeared in the literature. Building on the proposed filtering framework, we develop an experiment design procedure, adapted from experiment design results for discrete-time systems, where the piecewise constant 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.