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Supervised learning of perceptron and output feedback dynamic networks: a feedback analysis via the small gain theorem

机译:感知器和输出反馈动态网络的监督学习:基于小增益定理的反馈分析

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This paper provides a time-domain feedback analysis of the perceptron learning algorithm and of training schemes for dynamic networks with output feedback. It studies the robustness performance of the algorithms in the presence of uncertainties that might be due to noisy perturbations in the reference signals or due to modeling mismatch. In particular, bounds are established on the step-size parameters in order to guarantee that the resulting algorithms will behave as robust filters. The paper also establishes that an intrinsic feedback structure can be associated with the training schemes. The feedback configuration is motivated via energy arguments and is shown to consist of two major blocks: a time-variant lossless (i.e., energy preserving) feedforward path and a time-variant feedback path. The stability of the feedback structure is then analyzed via the small gain theorem, and choices for the step-size parameter in order to guarantee faster convergence are deduced by using the mean-value theorem. Simulation results are included to demonstrate the findings.
机译:本文提供了感知器学习算法和具有输出反馈的动态网络训练方案的时域反馈分析。它在存在不确定性的情况下研究算法的鲁棒性,这些不确定性可能是由于参考信号中的噪声扰动或由于建模不匹配所致。特别地,在步长参数上建立界限,以确保所得的算法将表现为鲁棒的滤波器。本文还确定了内在的反馈结构可以与训练方案相关联。反馈配置是通过能量参数来激发的,并且显示为由两个主要模块组成:时变无损(即节能)前馈路径和时变反馈路径。然后,通过小增益定理分析反馈结构的稳定性,并使用平均值定理推导步长参数以确保更快收敛。包括仿真结果以证明发现。

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