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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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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.
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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.
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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.
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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Strictly intermittent quantized control for fixed/predefined-time cluster lag synchronization of stochastic

Xuejiao Qin1, Haijun Jiang1, Jianlong Qiu2

  • 1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|December 8, 2022
PubMed
Summary

This study achieves fixed-time and predefined-time cluster lag synchronization for stochastic multi-weighted complex networks using strictly intermittent quantized control. The novel control strategy offers simpler and more economical solutions for synchronization tasks.

Keywords:
Cluster lag synchronizationFixed-timePredefined-timeStochastic multi-weighted complex networkStrictly intermittent quantized control

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Area of Science:

  • Complex Networks
  • Control Theory
  • Stochastic Systems

Background:

  • Synchronization is crucial in complex systems.
  • Stochastic multi-weighted complex networks (SMWCNs) present unique challenges.
  • Existing control methods may be complex or inefficient.

Purpose of the Study:

  • To achieve fixed-time (F-T) and predefined-time (P-T) cluster lag synchronization in SMWCNs.
  • To develop a novel strictly intermittent quantized control (SIQC) strategy.
  • To design simpler and more economical controllers.

Main Methods:

  • Mathematical induction and reduction to absurdity for proving stability.
  • Development of a novel F-T stability lemma with accurate settling time (ST) estimation.
  • Design of SIQC strategies for both F-T and P-T synchronization.

Main Results:

  • A novel F-T stability lemma was proven, enabling accurate ST estimation.
  • Simple conditions for F-T cluster lag synchronization were derived.
  • P-T cluster lag synchronization was achieved with a predefinable ST.
  • The proposed controllers are more economical as they deactivate the linear part during rest intervals.

Conclusions:

  • The proposed SIQC strategy effectively achieves F-T and P-T cluster lag synchronization in SMWCNs.
  • The developed control approach is simpler and more cost-effective than traditional methods.
  • Numerical examples validate the theoretical findings and the controller's effectiveness.