This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are feasible and provide superior performance guarantees with high probability. This results into the formulation of a stochastic optimization problem (P), which is intractable due to the unknown distribution of the uncertainty variables. By developing a distributionally robust optimization framework, we present an equivalent and yet tractable reformulation of (P). Further, we propose an efficient algorithm that provides online suboptimal data-driven solutions and guarantees performance with high probability. To illustrate the effectiveness of the proposed approach, we consider a highway speed-limit control problem. We then develop a set of data-driven speed controls that allow us to prevent traffic congestion with high probability. Finally, we employ the resulting control method on a traffic simulator to illustrate the effectiveness of this approach numerically.
翻译:本文研究一种数据驱动的预测控制,这种控制室系统有不确定性。随着对不确定变量的有限抽样测量的可及性,我们的目标是寻找可行的控制,提供高性能保障。这导致形成一个随机优化问题(P),由于不确定变量分布不明,这一问题难以解决。通过开发一个分布强大的优化框架,我们提出了一个相当和可移动的重塑(P)。此外,我们提出一个高效的算法,提供在线亚最佳数据驱动解决方案,并高概率地保证性能。为了说明拟议方法的有效性,我们考虑了一个高速公路速度限制控制问题。然后,我们开发了一套数据驱动速度控制系统,使我们能够以高概率防止交通拥堵。最后,我们对一个交通模拟器采用了相应的控制方法,以数字方式说明这种方法的有效性。