Data-Based System Analysis and Control of Flat Nonlinear Systems

TL;DR

This paper extends Willems' linear system trajectory representation to flat nonlinear systems, enabling data-based control and simulation without explicit model identification.

Contribution

It introduces a novel data-driven parametrization for all trajectories of flat nonlinear systems, facilitating control and simulation directly from input-output data.

Findings

Successful extension of Willems' linear results to nonlinear systems

Effective data-based control and simulation demonstrated

Numerical examples validate the approach

Abstract

Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In this paper, we extend this result to the class of discrete-time single-input single-output flat nonlinear systems. We propose a data-based parametrization of all trajectories using only input-output data. Further, we use this parametrization to solve the data-based simulation and output-matching control problems for the unknown system without explicitly identifying a model. Finally, we illustrate the main results with numerical examples.