Title: The Bayesian Separation Principle for Data-driven Control Show Chinese title

Title: 数据驱动控制的贝叶斯分离原理

Abstract: In this paper we investigate the existence of a separation principle between model identification and control design in the context of model predictive control. First, we clarify that such a separation principle holds asymptotically in the number of data in a Fisherian context, and show that it holds universally, i.e. regardless of the data size, in a Bayesian context. Then, by formulating model predictive control within a Gaussian regression framework, we describe how the Bayesian separation principle can be used to derive computable, uncertainty-aware expressions for the control cost and optimal input sequence, thereby bridging direct and indirect data-driven approaches. Numerical results in both linear and nonlinear scenarios illustrate that the proposed approach outperform nominal methods that neglect uncertainty, highlighting the advantages of incorporating uncertainty in the control design process. Show Chinese abstract

Abstract: 在本文中，我们研究了在模型预测控制背景下模型识别与控制设计之间的分离原理的存在性。 首先，我们明确指出，在费舍尔情境下，这种分离原理在数据数量上渐近成立，并表明在贝叶斯情境下，它普遍成立，即无论数据规模如何。 然后，通过在高斯回归框架内表述模型预测控制，我们描述了如何利用贝叶斯分离原理推导出可计算的、考虑不确定性的控制成本和最优输入序列表达式，从而弥合直接和间接的数据驱动方法之间的差距。 在线性和非线性场景中的数值结果表明，所提出的方法优于忽略不确定性的名义方法，突显了在控制设计过程中纳入不确定性的优势。