AI 中文总结
提出高斯行为随机行为建模框架，通过对高斯行为条件设定获预测方法，开发预测控制公式并推导置信界用于鲁棒控制，能恢复子空间预测控制，数据驱动预测控制可乐观考虑不确定性，数值研究验证方法优势。
AI 中文摘要
我们提出了一个随机行为建模框架，称为高斯行为，它用高斯噪声分量增强确定性线性时不变（LTI）行为。我们表明这个概念是随机行为的一个易于处理的子类，并且包含经典参数随机LTI状态空间系统模型作为特殊情况。类似于确定性LTI行为，该框架实现了简单且易于处理的随机数据驱动控制方法。为此，我们通过基于轨迹的已知部分对高斯行为进行条件设定来获得一种预测方法，该方法直接从轨迹数据的样本协方差中识别。基于此方法，我们开发了在前馈或干扰仿射反馈策略上进行优化的预测控制公式。结果表明这些公式是凸的。我们进一步推导了考虑偶然和认知不确定性的预测的有限样本置信界，并将其纳入一种鲁棒控制方法，为此获得了一个易于处理的凸上界。在这个框架内，当仅使用均值预测时恢复子空间预测控制，而数据驱动预测控制以乐观方式考虑预测不确定性。数值案例研究说明了所提出方法的优点。
英文摘要
We propose a stochastic behavioral modeling framework, termed Gaussian behaviors, which augments a deterministic linear time-invariant (LTI) behavior with a Gaussian noise component. We show that this notion is a tractable subclass of stochastic behaviors and encompasses classical parametric stochastic LTI state-space system models as special cases. Analogously to deterministic LTI behaviors, the framework enables simple and tractable stochastic data-driven control methods. To this end, we obtain a method for prediction by conditioning the Gaussian behavior on the known part of the trajectory, which is identified directly from the sample covariance of trajectory data. Building on this method, we develop predictive control formulations that optimize over feedforward or disturbance affine feedback policies. The resulting formulations are shown to be convex. We further derive a finite-sample confidence bound on the prediction accounting for both aleatoric and epistemic uncertainty, and incorporate it into a robust control method, for which a tractable convex upper bound is obtained. Within this framework, subspace predictive control is recovered when only the mean prediction is used, while data-enabled predictive control is shown to account for the prediction uncertainty in an optimistic fashion. Numerical case studies illustrate the benefits of the proposed methods.
