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

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.