用可逆神经网络实现未知非线性系统的可靠前馈跟踪控制。
Certified Feedforward Tracking for Unknown Nonlinear Systems via Invertible Neural Networks
- 用可逆神经网络建模未知系统，避免求解非凸反演问题
- 结合置信预测提供有限样本下的误差保证，降低跟踪误差
- 适用于部分状态测量的非线性系统，适合工业控制场景
本文针对未知非线性系统在部分状态测量下的周期跟踪问题，提出数据驱动的前馈控制认证方法。采用可逆神经网络（INN）作为未知系统的代理模型，避免了求解非凸反演问题，消除了相关反演误差，将跟踪误差认证转化为代理建模误差认证。随后应用置信预测，在有限样本下对代理模型误差提供概率保证，进而通过推导的跟踪误差界，获得前馈跟踪误差的边际证书。实验在具有非线性摩擦的直流电机驱动机械负载上验证了该方法的有效性。
原文摘要 · Abstract (English)
In this paper, we address the certification of datadriven feedforward control for periodic tracking of unknown nonlinear systems under partial state measurements. To this end, we adopt an invertible neural network (INN) as a surrogate for the unknown system. This choice allows us to bypass solving a nonconvex inversion problem, eliminating the associated inversion errors and reducing tracking error certification to a surrogate modeling problem. We then apply conformal prediction to provide finite-sample probabilistic guarantees on the surrogate modeling error which, through the derived tracking error bound, yield marginal certificates on feedforward tracking error. Finally, we demonstrate the approach on a DC-motor-driven mechanical load with nonlinear friction.
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