论文标题
使用扩展的DMD迈向可靠的基于数据的最佳和预测性控制
Towards reliable data-based optimal and predictive control using extended DMD
论文作者
论文摘要
尽管如今，基于Koopman的技术（例如扩展动态模式分解）在数据驱动的动态系统的近似中无处不在，但直到最近才建立了定量误差估计。为此，必须考虑到替代模型的生成中的两个错误源和仅有限的数据点。我们将近似误差的严格分析概括为控制设置，同时通过使用最近提出的双线性方法同时降低了维度诅咒的影响。特别是，我们建立了统一的界限，以依赖状态依赖性数量（例如约束或性能索引）的近似误差，从而启用具有保证的基于数据的最佳和预测性控制。
While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of error resulting from a finite dictionary and only finitely-many data points in the generation of the surrogate model have to be taken into account. We generalize the rigorous analysis of the approximation error to the control setting while simultaneously reducing the impact of the curse of dimensionality by using a recently proposed bilinear approach. In particular, we establish uniform bounds on the approximation error of state-dependent quantities like constraints or a performance index enabling data-based optimal and predictive control with guarantees.
