AI 中文总结
针对低信噪比下线性时变系统的在线数据驱动预测控制，提出基于ARX模型和卡尔曼滤波的贝叶斯框架，通过不变先验在遗忘旧数据时保持先验，实验验证其有效性。
AI 中文摘要
低信噪比（SNR）数据是线性时变系统在线数据驱动预测控制（DPC）面临的核心挑战。本文提出一种基于带外生输入的自回归模型（ARX）的贝叶斯在线DPC框架，该框架利用外部提供的先验信息，该先验编码了诸如平滑系统动力学和稳定性等归纳偏置，以在信噪比低时保障性能。ARX参数的后验估计通过卡尔曼滤波器随时间向前传播，其状态方程由自适应速率超参数定义，该超参数在线调整以跟踪底层系统动力学演化的速率。卡尔曼滤波器的后验均值和协方差决定了DPC的最终控制误差代价函数，该函数是二次代价函数的后验期望。关键在于，卡尔曼滤波器的过程方程被设计为，无论超参数如何自适应，先验分布随时间保持不变。因此，虽然旧数据被遗忘，但先验信息不会被遗忘。在时变二阶系统上的DPC跟踪实验验证了所提出方法的有效性。
英文摘要
Low signal-to-noise ratio (SNR) data is a core challenge of online Data-Driven Predictive Control (DPC) for linear, time-varying systems. This paper proposes a Bayesian, online DPC framework based on autoregressive models with exogenous inputs (ARX) that uses an externally-provided prior, which encodes inductive bias such as smooth system dynamics and stability, to safeguard performance when SNR is low. The posterior estimate of the ARX parameter is propagated forward in time using a Kalman filter with a state equation defined by an adaptation-rate hyperparameter, which is adjusted online to track the rate at which the underlying system dynamics evolve. The Kalman filter's posterior mean and covariance determine the DPC's Final Control Error cost function, which is the posterior expectation of the quadratic cost function. Critically, the Kalman filter's process equation is chosen so that, regardless of the hyperparameter adaptation, the prior distribution is invariant over time. Thus, while old data is forgotten, the prior is not. DPC tracking experiments on a time-varying second-order system demonstrate the efficacy of the proposed method.
Comments8 pages, 3 figures, conference paper (CDC)
