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.
A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees
University of Stuttgart（斯图加特大学）；Center for Integrated Quantum Science and Technology (IQST), University of Stuttgart（斯图加特大学综合量子科学与技术中心）；University of Oxford（牛津大学）
Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems
Cornell University（康奈尔大学）；Imperial College London（帝国理工学院）；University of Stuttgart（斯图加特大学）；University of Washington Seattle（华盛顿大学西雅图分校）；Amazon Inc.（亚马逊公司）
An overview of Koopman-based control: From error bounds to closed-loop guarantees
University of Stuttgart（斯图加特大学）；Technische Universitat Ilmenau（伊尔梅瑙工业大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Chemnitz University of Technology（开姆尼茨工业大学）
Cable Estimation-Based Control for Wire-Borne Underactuated Brachiating Robots: A Combined Direct-Indirect Adaptive Robust Approach
Institute for Robotics and Intelligent Machines, Georgia Institute of Technology（佐治亚理工学院机器人与智能机器研究所）；Stanford University（斯坦福大学）；Georgia Tech Research Institute（佐治亚理工学院研究所）；Georgia Institute of Technology（佐治亚理工学院）
