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相关概念视频

Linear time-invariant Systems01:23

Linear time-invariant Systems

289
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...
289
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

110
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....
110
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

101
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
101
Second Order systems II01:18

Second Order systems II

130
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.
130
Classification of Systems-I01:26

Classification of Systems-I

215
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
215
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

437
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....
437

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相关实验视频

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Experimental Methods to Study Human Postural Control
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一种针对受非静止噪声影响的非线性动态系统的强有力的稀疏识别方法.

Zhihang Hao1, Chunhua Yang1, Keke Huang1

  • 1School of Automation, Central South University, Changsha 410083, China.

Chaos (Woodbury, N.Y.)
|August 7, 2023
PubMed
概括

这项研究引入了一种用于从噪音数据中识别非线性动态的新方法. 拟议的方法通过强大处理非静止噪声来提高准确性,改善稀疏识别结果.

科学领域:

  • 科学与工程科学与工程
  • 动态系统理论 动态系统理论
  • 数据驱动的建模数据驱动的建模

背景情况:

  • 从数据中识别非线性系统动态是至关重要的,但具有挑战性.
  • 噪声数据,特别是非静止噪声,显著降低了传统识别方法的准确性.
  • 现有的技术往往无法充分解决非静止噪声对系统识别的影响.

研究的目的:

  • 开发一种可靠的方法,用于从被非静止噪声污染的数据中识别非线性动态.
  • 为了提高在噪声存在的情况下稀疏识别动态的准确性和可靠性.
  • 提出一种新的数学框架,以量化解释非静止噪声.

主要方法:

  • 提出了一个加权的l1-规则化和不敏感的损失函数,用于可靠的稀疏识别.
  • 使用稀疏识别数学模型制定了强大的识别问题.
  • 开发了一种使用平滑近似和交替方向乘法方法的高效优化算法.
  • 利用一种新型加权的l1-调节和不敏感的损失函数来减轻非静止噪声效应.

主要成果:

  • 拟议的方法有效地减轻了非静止噪声的不利影响.
  • 与传统的损失函数相比,实现了结果的增强稀疏性.

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  • 在各种非线性动态系统的广泛实验中证明了卓越的识别准确性.
  • 在强大的识别任务中超越了最先进的方法.

    • 结论:

    • 开发的基于权重l1调节和不敏感损失函数的稀疏识别方法提供了更好的准确性和稳定性.
    • 该方法为从噪音数据集中识别非线性动态提供了可靠的解决方案.
    • 这项工作通过有效处理非静止噪声,推进了数据驱动系统识别领域.