循环神经网络的稳定性分析,时间延迟变化,基于灵活的负判定二次函数方法
IEEE transactions on neural networks and learning systems
|November 3, 2023
概括
本研究提出了一种新方法来分析具有时间变化的延迟的循环神经网络 (RNN) 的稳定性. 这些发现为这些复杂系统提供了一个不那么保守的稳定性标准.
科学领域:
- 控制理论 控制理论
- 人工智能的人工智能
- 神经网络的神经网络的神经网络
背景情况:
- 循环神经网络 (RNN) 对于连续的数据处理至关重要.
- 具有不同时间延迟的RNN的稳定性分析是一个重大挑战.
- 现有的稳定性分析方法可能过于保守.
研究的目的:
- 调查RNN的稳定性问题与时间变化的延迟.
- 制定一个不那么保守的稳定性标准.
- 证明拟议方法的有效性.
主要方法:
- 引入灵活性因子,用于一种新的负判定二次函数方法.
- 将积分不等式应用到Lyapunov-Krasovskii函数 (LKF) 导数的结合上.
- 对延迟RNN的稳定性标准的推导.
主要成果:
- 提出了一种灵活的负确定二次函数方法,减少保守主义.
- 确定了LKF衍生品的准确上限.
- 对于延迟的RNN来说,一个不那么保守的稳定性标准是得到的.
结论:
- 拟议的方法为具有时间变化的延迟的RNN提供了改进的稳定性分析.
- 衍生稳定性标准比现有方法要保守得多.
- 数字示例验证了拟议方法的有效性和优越性.
相关概念视频
01:19Routh-Hurwitz Criterion II
260
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
260
01:18Second Order systems II
115
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
115
01:07Time-Domain Interpretation of PD Control
120
Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
Consider the example of control of motor torque. Initially, a positive...
120
01:26Linear Approximation in Frequency Domain
94
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
94
01:23Linear time-invariant Systems
263
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
263
01:31Classification of Systems-II
150
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
150