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.

翻译：本文提出了一种针对双线性系统的间接数据驱动控制的端到端算法，并具备稳定性保证。我们考虑所收集的独立同分布数据受可能具有无界支撑的概率噪声影响的情况，并利用统计学习理论工具推导出有限样本辨识误差界。为此，我们通过在数据采集阶段对控制输入进行特定选择，将双线性辨识问题转化为求解一组线性和仿射辨识问题。我们针对各个矩阵和椭球界分别提供了先验以及依赖于数据的有限样本辨识误差界，这两种界在结构上都适用于控制。进一步地，我们将推导出的辨识误差界的结构集成到鲁棒控制器设计中，以获得指数稳定的闭环系统。通过大量数值研究，我们展示了控制器设计与推导出的辨识误差界之间的相互作用。此外，我们注意到所得结果与通过库普曼算子理论对一般非线性系统进行间接数据驱动控制存在有吸引力的联系，并讨论了我们的结果如何应用于该设定中。