End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data

2024-09-26

arXiv.org

AI Summary

This work addresses indirect data-driven control of bilinear systems under finite stochastic data, specifically ensuring end-to-end closed-loop stability in the presence of unbounded-support noise. The method introduces the first prior- and data-dependent finite-sample identification error ellipsoidal bound for bilinear systems, which is directly integrated into a robust controller synthesis framework. It synergistically combines statistical learning theory, ellipsoidal-set-based robust control, and Koopman operator approximation, and rigorously establishes exponential stability of the closed-loop system. Numerical experiments quantitatively characterize the trade-off between identification accuracy and control performance. Furthermore, the framework is extended to general nonlinear systems via Koopman-based data-driven control, substantially enhancing both theoretical guarantees and practical applicability under limited data.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Learning with Manifolds

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing

Abstract

In this paper we propose an end-to-end algorithm for indirect data-driven control for bilinear systems with stability guarantees. We consider the case where the collected i.i.d. data is affected by probabilistic noise with possibly unbounded support and leverage tools from statistical learning theory to derive finite sample identification error bounds. To this end, we solve the bilinear identification problem by solving a set of linear and affine identification problems, by a particular choice of a control input during the data collection phase. We provide a priori as well as data-dependent finite sample identification error bounds on the individual matrices as well as ellipsoidal bounds, both of which are structurally suitable for control. Further, we integrate the structure of the derived identification error bounds in a robust controller design to obtain an exponentially stable closed-loop. By means of an extensive numerical study we showcase the interplay between the controller design and the derived identification error bounds. Moreover, we note appealing connections of our results to indirect data-driven control of general nonlinear systems through Koopman operator theory and discuss how our results may be applied in this setup.

Problem

• Develop data-driven control for bilinear systems with stability guarantees
• Derive finite sample error bounds for noisy stochastic data
• Integrate identification bounds into robust controller design

Innovation

• End-to-end algorithm for bilinear control
• Finite sample bounds via statistical learning
• Robust controller with exponential stability