论文标题
数据驱动的机会限制了使用内核分布嵌入的控制
Data-Driven Chance Constrained Control using Kernel Distribution Embeddings
论文作者
论文摘要
我们提出了一种数据驱动的算法，用于有效地计算出随机控制策略，以限制最佳控制问题。我们的方法利用了内核分布嵌入的理论，该理论允许将期望运算符代表繁殖的内核希尔伯特空间中的内部产品。该框架可以使用系统中观察到的轨迹的数据集近似地重新编译原始问题，而无需对系统动力学的参数化或不确定性结构施加先前的假设。通过在随机开环控制轨迹的有限子集上进行优化，我们在控制参数上放松了线性程序的原始问题，可以使用标准凸优化技术有效地解决。我们证明了我们在杂乱的环境中导航的非线性非马克维亚动力学的系统模拟中提出的方法。
We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.
