Anderson Charles W, Young Peter Michael, Buehner Michael R, Knight James N, Bush Keith A, Hittle Douglas C
Department of Computer Science, Colorado State University, Fort Collins, CO 80523-1873, USA.
IEEE Trans Neural Netw. 2007 Jul;18(4):993-1002. doi: 10.1109/TNN.2007.899520.
The applicability of machine learning techniques for feedback control systems is limited by a lack of stability guarantees. Robust control theory offers a framework for analyzing the stability of feedback control loops, but for the integral quadratic constraint (IQC) framework used here, all components are required to be represented as linear, time-invariant systems plus uncertainties with, for IQCs used here, bounded gain. In this paper, the stability of a control loop including a recurrent neural network (NN) is analyzed by replacing the nonlinear and time-varying components of the NN with IQCs on their gain. As a result, a range of the NN's weights is found within which stability is guaranteed. An algorithm is demonstrated for training the recurrent NN using reinforcement learning and guaranteeing stability while learning.
机器学习技术在反馈控制系统中的适用性因缺乏稳定性保证而受到限制。鲁棒控制理论提供了一个分析反馈控制回路稳定性的框架，但对于此处使用的积分二次约束（IQC）框架，所有组件都必须表示为线性、时不变系统加上不确定性，对于此处使用的IQC，增益是有界的。在本文中，通过用IQC对其增益进行替换来分析包含递归神经网络（NN）的控制回路的稳定性。结果，找到了一系列能保证稳定性的NN权重范围。展示了一种使用强化学习训练递归NN并在学习过程中保证稳定性的算法。
