一个交换系统模型,用于指数稳定性和延迟神经网络的分散性
概括
这项研究通过将它们建模为交换系统来增强神经网络稳定性分析,以对时间变化的延迟进行分析. 新的标准确保了延迟神经网络 (DNN) 的指数稳定性和消散性.
科学领域:
- 控制系统工程 控制系统工程
- 计算神经科学是一种神经科学.
- 应用数学 应用数学 应用数学
背景情况:
- 有时间变化的延迟的神经网络带来了重大的稳定性挑战.
- 现有的分析这些系统的方法往往缺乏足够的关于延迟动态的信息.
- 利亚普诺夫-克拉索夫斯基函数 (LKF) 对于稳定性分析至关重要,但需要对时间变化的延迟进行仔细的构建.
研究的目的:
- 开发新的标准,以确保延迟神经网络 (DNN) 中的指数稳定性和消散性,延迟时间可变.
- 通过结合有关延迟及其衍生物的更多信息来改进DNN的分析.
- 为构建LKF提供一个更灵活的框架.
主要方法:
- 将延迟神经网络 (DNN) 建模为基于延迟导数的符号的两种模式的切换系统.
- 使用平均停留时间 (ADT) 技术来分析开关系统.
- 基于构建的LKF,开发指数稳定性和指数散射性的新标准.
主要成果:
- 导出了DNN的指数稳定性和指数消散性以及具有时间变化延迟的几个新标准.
- 拟议的开关系统模型在LKF构造中提供了更大的灵活性,允许每个模式有不同的Lyapunov矩阵.
- 衍生的标准在基准示例和实际控制系统中显示出优于现有方法的优势.
结论:
- 建议的交换系统方法和ADT技术有效地解决了DNN稳定性分析中时间变化的延迟所带来的挑战.
- 新的标准为确保指数稳定性和散射性提供了一个强大的和实用的方法.
- 这些发现对复杂神经网络系统的可靠设计和控制有影响.
相关概念视频
Second Order systems II
173
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.
173
BIBO stability of continuous and discrete -time systems
521
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
521
Linear Approximation in Frequency Domain
135
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....
135
Classification of Systems-II
242
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,
242
Current Growth And Decay In RL Circuits
4.0K
The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...
4.0K
Transient and Steady-state Response
278
In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...
278


