Issues with Input-Space Representation in Nonlinear Data-Based Dissipativity Estimation

TL;DR

This paper reviews existing data-based methods for estimating dissipativity in nonlinear systems, highlights their limitations, and introduces a new approach that improves robustness and sample efficiency, supported by numerical case studies.

Contribution

The paper analyzes the limitations of current delta-covering methods and proposes a novel robustness quantification approach for machine learning-based dissipativity estimation.

Findings

Delta-covering methods have intractable sample complexity-robustness trade-offs.

The new robustness quantification method improves the trade-off between robustness and sample complexity.

Numerical case studies validate the effectiveness of the proposed approach.

Abstract

In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based dissipativity estimation of nonlinear systems. The interplay between the underlying assumptions of these methods and their sample complexity is investigated. It is shown that methods based on delta-covering result in an intractable trade-off between sample complexity and robustness. A new method is proposed to quantify the robustness of machine learning-based dissipativity estimation. It is shown that this method achieves a more tractable trade-off between robustness and sample complexity. Several numerical case studies demonstrate the results.