论文标题
非线性系统的强大和内核化的数据支持预测控制
Robust and Kernelized Data-Enabled Predictive Control for Nonlinear Systems
论文作者
论文摘要
本文提出了一种强大的，内核化的启用数据的预测控制（ROKDEEPC）算法，以对仅使用输入和输出数据的非线性系统执行非模型的最佳控制。该算法结合了可靠的预测性控制和通过正规内核方法启用的非线性系统的非参数表示。后者基于通过代表定理隐含地学习系统的非线性行为。我们的方法不是寻求模型然后执行控制设计，而是直接从数据转到控制。这使我们能够通过考虑最低最大优化问题来计算最佳控制序列，从而对数据中的不确定性进行鲁棒性。我们表明，通过纳入适当的不确定性集，这个最小的最大问题可以重新构成非概念但结构化最小化问题。通过利用其结构，我们提出了一种预计的梯度下降算法，以有效解决此问题。最后，我们在两个非线性示例系统上测试了Rokdeepc-一个学术案例研究和一个供应非线性负载的网格的转换器 - 并将其与一些现有的非线性数据驱动的预测性控制方法进行比较。
This paper presents a robust and kernelized data-enabled predictive control (RoKDeePC) algorithm to perform model-free optimal control for nonlinear systems using only input and output data. The algorithm combines robust predictive control and a non-parametric representation of nonlinear systems enabled by regularized kernel methods. The latter is based on implicitly learning the nonlinear behavior of the system via the representer theorem. Instead of seeking a model and then performing control design, our method goes directly from data to control. This allows us to robustify the control inputs against the uncertainties in data by considering a min-max optimization problem to calculate the optimal control sequence. We show that by incorporating a proper uncertainty set, this min-max problem can be reformulated as a nonconvex but structured minimization problem. By exploiting its structure, we present a projected gradient descent algorithm to effectively solve this problem. Finally, we test the RoKDeePC on two nonlinear example systems - one academic case study and a grid-forming converter feeding a nonlinear load - and compare it with some existing nonlinear data-driven predictive control methods.
