具有轉移學習的數據驅動迭代學習控制

Abstract

由數據驅動的迭代學習控制可以通過消除參數系統表示中的擬合誤差，並實現了比基於模型的迭代學習控制更優秀的軌跡追蹤性能。在頻域中，目前現有的數據驅動方法以較低的成本獲取非參數化頻率響應函數並實現快速有效的學習。然而數據的品質對演算法的性能有著明顯的影響。另一個顯著的缺點是每當追蹤的軌跡改變時，即使在先前相同的頻率成分上已經進行過學習，學習過程仍然會被重置。此外將這些從單變數系統中的方法延伸到具有不可忽略耦合性的多變數系統並不直觀。因此本研究旨在通過採用頻譜分析（SPA）來解決由數據驅動的 ILC 中的上述挑戰。通過減輕量測雜訊的影響，SPA改善了由數據驅動的學習濾波器設計。並且使用迭代變化的學習增益可以實現快速且穩健的收斂表現。同時提出了在頻域中的轉移學習策略，其中先前設計好的學習濾波器在特定頻率中的資訊將被保留並用於加速後續任務的收斂速度。所提出的基於 SPA 的 ILC 演算法也可以擴展到多輸入多輸出（MIMO）框架，並透過複數矩陣分析確保其收斂。該方法在光學振鏡系統上得到了實驗驗證，展示了更好的軌跡追蹤性能、轉移學習功能以及對 MIMO 系統的適用性。

Data-driven iterative learning control (ILC) can achieve improved tracking performance over model-based ILC by eliminating fitting error from parametric system representations. Existing data-driven approaches in frequency domain take advantage of the affordability and speed associated with acquiring non-parametric frequency response function data for effective learning. However, the quality of data significantly influences the achievable performance. Additionally, a notable drawback is that learning is reset whenever the tracked trajectory changes, despite having learned similar frequency contents before. Extending these approaches to multivariate systems with non-negligible coupling is also not straightforward. This paper aims to address the aforementioned challenges in data-driven ILC by employing spectral analysis (SPA), which improves the learned data-driven inversion by mitigating the measurement noise. Fast and robust convergence is made possible through an iteration-varying learning gain. Also proposed is a transfer learning strategy in the frequency domain, wherein the inversion learned in specific frequency bin(s) will be preserved and utilized to expedite convergence in subsequent tasks. The presented ILC algorithm based on SPA naturally extends to the multi-input multi-output (MIMO) framework, and the convergence can be ensured by complex-valued matrix analysis. The methodology is experimentally validated on a galvanometer mirror steering system, showcasing enhanced performance, transfer learning capabilities, and applicability to MIMO systems.