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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Nonsmooth Neural Network for Convex Time-Dependent Constraint Satisfaction Problems
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Nonsmooth Neural Network for Convex Time-Dependent Constraint Satisfaction Problems

机译：凸时间相关约束满足问题的非光滑神经网络

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摘要

This paper introduces a nonsmooth (NS) neural network that is able to operate in a time-dependent (TD) context and is potentially useful for solving some classes of NS-TD problems. The proposed network is named nonsmooth time-dependent network (NTN) and is an extension to a TD setting of a previous NS neural network for programming problems. Suppose , , is a nonempty TD convex feasibility set defined by TD inequality constraints. The constraints are in general NS (nondifferentiable) functions of the state variables and time. NTN is described by the subdifferential with respect to the state variables of an NS-TD barrier function and a vector field corresponding to the unconstrained dynamics. This paper shows that for suitable values of the penalty parameter, the NTN dynamics displays two main phases. In the first phase, any solution of NTN not starting in at is able to reach the moving set in finite time , whereas in the second phase, the solution tracks the moving set, i.e., it stays within for all subsequent times . NTN is thus able to find an exact feasible solution in finite time and also to provide an exact feasible solution for subsequent times. This new and peculiar dynamics displayed by NTN is potentially useful for addressing some significant TD signal processing tasks. As an illustration, this paper discusses a number- of examples where NTN is applied to the solution of NS-TD convex feasibility problems.
机译：本文介绍了一种非平稳（NS）神经网络，该网络能够在时间相关（TD）上下文中运行，并且对于解决某些类别的NS-TD问题可能很有用。所提出的网络被称为非平稳时间相关网络（NTN），它是对以前的用于编程问题的NS神经网络的TD设置的扩展。假设是由TD不等式约束定义的非空TD凸可行性集。约束通常是状态变量和时间的NS（不可微分）函数。 NTN由关于NS-TD屏障函数的状态变量的亚微分和对应于无约束动态的矢量场描述。本文表明，对于惩罚参数的合适值，NTN动态显示两个主要阶段。在第一阶段中，任何不从开始的NTN解决方案都可以在有限时间内到达移动集合，而在第二阶段中，该解决方案跟踪移动集合，即它在所有后续时间都停留在此范围内。因此，NTN能够在有限时间内找到精确可行的解决方案，并且还可以为后续时间提供精确可行的解决方案。 NTN显示的这种新奇的动态特性可能对解决一些重要的TD信号处理任务很有用。作为说明，本文讨论了将NTN应用于解决NS-TD凸可行性问题的许多示例。

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