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Lur'e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity

机译:具有多层感知器和递归神经网络的Lur'e系统:绝对稳定性和耗散性

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摘要

Sufficient conditions for absolute stability and dissipativity of continuous-time recurrent neural networks with two hidden layers are presented. In the autonomous case this is related to a Lur'e system with multilayer perceptron nonlinearity. Such models are obtained after parametrizing general nonlinear models and controllers by a multilayer perceptron with one hidden layer and representing the control scheme in standard plant form. The conditions are expressed as matrix inequalities and can be employed for nonlinear H/sub /spl infin// control and imposing closed-loop stability in dynamic backpropagation.
机译:提出了具有两个隐藏层的连续时间递归神经网络的绝对稳定性和耗散性的充分条件。在自主情况下,这与具有多层感知器非线性的Lur'e系统有关。这些模型是通过使用具有一个隐藏层并以标准工厂形式表示控制方案的多层感知器对通用非线性模型和控制器进行参数化后获得的。这些条件表示为矩阵不等式,可用于非线性H / sub / spl infin //控制,并在动态反向传播中施加闭环稳定性。

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