用满足微分方程的高斯过程做预测控制，实现稳定跟踪。
Physics-informed Gaussian Processes as Linear Model Predictive Controller
- 将高斯过程约束在常系数线性微分方程上，构建物理一致的先验
- 通过设定目标点条件化后验，实现带软约束的实时控制
- 理论保证开环稳定，适合需要可靠轨迹的工业控制场景
我们提出一种新算法，用于线性时不变系统的轨迹跟踪控制。控制器基于满足常系数线性常微分方程组的高斯过程（GP）构建，控制输入通过将先验GP对设定点进行条件化获得，即“控制即推断”。所提出的模型预测控制方案通过引入虚拟设定点，在后验高斯过程中嵌入逐点软约束。理论上，我们利用贝叶斯推断的一般结果，证明该控制器对最优控制问题具有开环稳定性，并在数值例子中验证了该结论。
原文摘要 · Abstract (English)
We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with constant coefficients. Control inputs for tracking are determined by conditioning the prior GP on the setpoints, i.e. control as inference. The resulting Model Predictive Control scheme incorporates pointwise soft constraints by introducing virtual setpoints to the posterior Gaussian process. We show theoretically that our controller satisfies open-loop stability for the optimal control problem by leveraging general results from Bayesian inference and demonstrate this result in a numerical example.
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