In Model Predictive Control (MPC), discrepancies between the actual system and the predictive model can lead to substantial tracking errors and significantly degrade performance and reliability. While such discrepancies can be alleviated with more complex models, this often complicates controller design and implementation. By leveraging the fact that many trajectories of interest are periodic, we show that perfect tracking is possible when incorporating a simple observer that estimates and compensates for periodic disturbances. We present the design of the observer and the accompanying tracking MPC scheme, proving that their combination achieves zero tracking error asymptotically, regardless of the complexity of the unmodelled dynamics. We validate the effectiveness of our method, demonstrating asymptotically perfect tracking on a high-dimensional soft robot with nearly 10,000 states and a fivefold reduction in tracking errors compared to a baseline MPC on small-scale autonomous race car experiments.

翻译：在模型预测控制（MPC）中，实际系统与预测模型之间的偏差会导致显著的跟踪误差，并严重降低控制性能与可靠性。虽然采用更复杂的模型可以缓解此类偏差，但这往往增加了控制器设计与实现的复杂性。利用许多感兴趣轨迹具有周期性的特点，我们证明：通过引入一个能够估计并补偿周期性扰动的简单观测器，可以实现完美跟踪。本文提出了该观测器及其配套的跟踪MPC方案，并从理论上证明两者结合能使跟踪误差渐近趋于零，且不受未建模动态复杂程度的影响。我们通过实验验证了该方法的效果：在包含近10,000个状态的高维软体机器人上实现了渐近完美跟踪；在小型自主赛车实验中，与基准MPC相比，跟踪误差降低了五倍。