Linearity of Koopman operators and simplicity of their estimators coupled with model-reduction capabilities has lead to their great popularity in applications for learning dynamical systems. While nonparametric Koopman operator learning in infinite-dimensional reproducing kernel Hilbert spaces is well understood for autonomous systems, its control system analogues are largely unexplored. Addressing systems with control inputs in a principled manner is crucial for fully data-driven learning of controllers, especially since existing approaches commonly resort to representational heuristics or parametric models of limited expressiveness and scalability. We address the aforementioned challenge by proposing a universal framework via control-affine reproducing kernels that enables direct estimation of a single operator even for control systems. The proposed approach, called control-Koopman operator regression (cKOR), is thus completely analogous to Koopman operator regression of the autonomous case. First in the literature, we present a nonparametric framework for learning Koopman operator representations of nonlinear control-affine systems that does not suffer from the curse of control input dimensionality. This allows for reformulating the infinite-dimensional learning problem in a finite-dimensional space based solely on data without apriori loss of precision due to a restriction to a finite span of functions or inputs as in other approaches. For enabling applications to large-scale control systems, we also enhance the scalability of control-Koopman operator estimators by leveraging random projections (sketching). The efficacy of our novel cKOR approach is demonstrated on both forecasting and control tasks.

Automated driving systems are often used for lane keeping tasks. By these systems, a local path is planned ahead of the vehicle. However, these paths are often found unnatural by human drivers. We propose a linear driver model, which can calculate node points that reflect the preferences of human drivers and based on these node points a human driver preferred motion path can be designed for autonomous driving. The model input is the road curvature. We apply this model to a self-developed Euler-curve-based curve fitting algorithm. Through a case study, we show that the model based planned path can reproduce the average behavior of human curve path selection. We analyze the performance of the proposed model through statistical analysis that shows the validity of the captured relations.