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相关概念视频

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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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,...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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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....
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Second Order systems II01:18

Second Order systems II

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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.
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Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
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Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

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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...
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Feedback control systems01:26

Feedback control systems

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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
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在残余误差下对非线性H2和H∞最佳控制问题进行稀疏连续近似.

Zhong Wang1, Yan Li1, Yuqing Qiu1

  • 1Department of Navigation, Guidance, and Control, Northwestern Polytechnical University, Xi'an, 710129, PR China.

ISA transactions
|December 9, 2023
PubMed
概括
此摘要是机器生成的。

本研究介绍了一种稀疏连续近似方法,用于解决非线性最佳控制问题 (OCP),使用汉密尔顿-雅各比-贝尔曼 (HJB) 和汉密尔顿-雅各比-伊萨克斯 (HJI) 方程. 该方法提高了H2和H-infinity控制的融合和计算效率.

关键词:
这就是HJB方程.这就是HJI方程.最佳的控制控制是最好的控制.强大的控制控制.一个接一个的近似.

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科学领域:

  • 控制理论 控制理论
  • 应用数学 应用数学 应用数学
  • 数字分析 数字分析

背景情况:

  • 顺序近似技术对于在最佳控制问题 (OCP) 中解决非线性汉密尔顿 - 雅各比 - 贝尔曼 (HJB) 和汉密尔顿 - 雅各比 - 艾萨克斯 (HJI) 方程至关重要.
  • 由于非线性H2和H-infinity OCPs中的残余错误和计算复杂性,现有的方法面临着趋同的挑战.

研究的目的:

  • 为无限地平线的非线性H2和H-infinity OCPs提出一个统一的表述和一种新的稀疏连续近似方法.
  • 解决由剩余错误引起的融合问题,并减少现有数值方法的计算负担.

主要方法:

  • 在非线性H2和H-无限OCP中,HJB/HJI部分微分方程 (PDEs) 的统一公式.
  • 不线性PDEs转换为线性PDEs的序列,可通过初始值问题在点上解决.
  • 纳入额外的约束,以确保结合,尽管残余错误.
  • 利用稀疏的基于网格的拼接点和基础函数,以实现高效的数值实现.

主要成果:

  • 提出的方法将复杂的非线性PDEs转换为一系列更简单的线性PDEs.
  • 即使存在剩余错误,通过额外的约束来保证趋同.
  • 使用稀疏网格技术实现了高效的数值实现.
  • 模拟证明了拟议方法的有效性.

结论:

  • 稀疏连续近似方法为解决非线性H2和H无限度OCP提供了有效和计算效率高的方法.
  • 统一的表述和趋同保证使该方法在实际应用中具有稳定性.
  • 使用稀疏网格显著提高了解决HJB/HJI方程的数值处理能力.