Sufficient Conditions for Persistency of Excitation with Step and ReLU Activation Functions
Sufficient Conditions for Persistency of Excitation with Step and ReLU Activation Functions
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DOI：
10.1109/cdc51059.2022.9992794
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Tyler Lekang;Andrew G. Lamperski
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文献类型：
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作者：
Tyler Lekang;Andrew G. Lamperski
本文定义了几何准则，然后用这些准则建立了由具有阶跃或ReLU激活函数的单隐层神经网络构造的向量函数具有激励持续性的充分条件。我们表明，当采用参考系统跟踪时，这些条件成立，这在自适应控制中通常是这样做的。对一类具有线性参数化激活的系统进行了数值验证，结果表明，在满足充分条件的情况下，参数估计收敛于真值。
This paper defines geometric criteria which are then used to establish sufficient conditions for persistency of excitation with vector functions constructed from single hidden-layer neural networks with step or ReLU activation functions. We show that these conditions hold when employing reference system tracking, as is commonly done in adaptive control. We demonstrate the results numerically on a system with linearly parameterized activations of this type and show that the parameter estimates converge to the true values with the sufficient conditions met.