In this paper, we consider the design of data-driven predictive controllers for nonlinear systems from input-output data via linear-in-control input Koopman lifted models. Instead of identifying and simulating a Koopman model to predict future outputs, we design a subspace predictive controller in the Koopman space. This allows us to learn the observables minimizing the multi-step output prediction error of the Koopman subspace predictor, preventing the propagation of prediction errors. To avoid losing feasibility of our predictive control scheme due to prediction errors, we compute a terminal cost and terminal set in the Koopman space and we obtain recursive feasibility guarantees through an interpolated initial state. As a third contribution, we introduce a novel regularization cost yielding input-to-state stability guarantees with respect to the prediction error for the resulting closed-loop system. The performance of the developed Koopman data-driven predictive control methodology is illustrated on a nonlinear benchmark example from the literature.

通过线性控制输入Koopman提升模型从输入-输出数据中设计数据驱动的非线性系统预测控制器，以学习最小化Koopman子空间预测器的多步输出预测误差的可观测量，并通过插值初始状态获得递归可行性保证和输入与状态稳定性保证。在文献综述中，通过非线性基准示例展示了Koopman数据驱动预测控制方法的性能。

具有鲁棒稳定性和递归可行性保证的Koopman数据驱动预测控制