论文标题
通过LQ重现内核来解释双riccati方程
Interpreting the dual Riccati equation through the LQ reproducing kernel
论文作者
论文摘要
在这项研究中，我们提供了对线性季度（LQ）最佳控制问题的双重差分方程的解释。采用新的观点，我们表明LQ最佳控制可以看作是在受控轨迹空间上的回归问题，并且后者具有非常自然的结构，作为繁殖的内核Hilbert Space（RKHS）。然后，双riccati方程描述了当初始时间变化时LQ重现内核值的变化。这揭示了控制理论与内核方法之间的新连接，这是一个广泛用于机器学习的领域。
In this study, we provide an interpretation of the dual differential Riccati equation of Linear-Quadratic (LQ) optimal control problems. Adopting a novel viewpoint, we show that LQ optimal control can be seen as a regression problem over the space of controlled trajectories, and that the latter has a very natural structure as a reproducing kernel Hilbert space (RKHS). The dual Riccati equation then describes the evolution of the values of the LQ reproducing kernel when the initial time changes. This unveils new connections between control theory and kernel methods, a field widely used in machine learning.
