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.

翻译：本文通过线性控制输入的Koopman提升模型，研究了基于输入-输出数据对非线性系统设计数据驱动预测控制器的问题。与辨识和仿真Koopman模型以预测未来输出不同，我们在Koopman空间中设计了一种子空间预测控制器。这使得我们能够学习最小化Koopman子空间预测器多步输出预测误差的可观测变量，从而避免预测误差的传播。为避免因预测误差导致预测控制方案失去可行性，我们在Koopman空间中计算了终端代价和终端集合，并通过插值初始状态获得了递归可行性保证。作为第三项贡献，我们引入了一种新型正则化代价函数，使得闭环系统相对于预测误差具有输入-状态稳定性保证。所提出的Koopman数据驱动预测控制方法的性能已在文献中一个非线性基准案例上得到验证。