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：本文提出一种具有稳定性保证的双线性系统间接数据驱动控制端到端算法。我们考虑所收集的独立同分布数据受可能无界支撑概率噪声影响的情形，并利用统计学习理论工具推导有限样本辨识误差界。为此，我们通过在数据采集阶段特定控制输入的选择，将双线性辨识问题转化为一组线性与仿射辨识问题进行求解。我们为各独立矩阵提供先验及数据依赖的有限样本辨识误差界，同时给出适用于控制结构设计的椭球界。进一步地，我们将推导出的辨识误差界结构整合至鲁棒控制器设计中，从而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所得辨识误差界之间的相互作用关系。此外，我们指出本研究结果与基于Koopman算子理论的通用非线性系统间接数据驱动控制存在显著关联，并探讨了如何在此框架下应用我们的研究成果。