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Related Concept Videos

Classification of Systems-II01:31

Classification of Systems-II

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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,
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Neural Circuits01:25

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Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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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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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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Convolution: Math, Graphics, and Discrete Signals01:24

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
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BIBO stability of continuous and discrete -time systems01:24

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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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Finite-time H∞ output synchronization for DCRDNNs with multiple delayed and adaptive output couplings.

Qian Qiu1, Yin Chen2, Housheng Su3

  • 1School of Artificial Intelligence, Henan University, Zhengzhou 450046, China.

Neural Networks : the Official Journal of the International Neural Network Society
|January 9, 2025
PubMed
Summary

This study addresses finite-time H∞ output synchronization in complex neural networks with adaptive couplings and disturbances. New adaptive laws and controllers ensure synchronization, validated by simulations.

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DCRDNNsFTHOSFTOSHOSMultiple delayed and adaptive output couplings

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Area of Science:

  • Control Systems Engineering
  • Computational Neuroscience
  • Applied Mathematics

Background:

  • Reaction-diffusion neural networks (DCRDNNs) are crucial for modeling complex spatio-temporal dynamics.
  • Synchronization of DCRDNNs is essential for distributed information processing and secure communication.
  • Existing methods often struggle with finite-time convergence and external disturbances.

Purpose of the Study:

  • To investigate and solve the finite-time H∞ output synchronization (FTHOS) problem for DCRDNNs.
  • To develop adaptive control strategies for systems with multiple delayed and adaptive output couplings.
  • To analyze synchronization performance under external disturbances.

Main Methods:

  • Design of an adaptive law to adjust output coupling weights based on output information.
  • Development of a controller to achieve FTHOS.
  • Formulation of a corollary for finite-time output synchronization (FTOS) in the absence of disturbances.
  • Proposal of a novel adaptive scheme for H∞ output synchronization (HOS) with delayed couplings.

Main Results:

  • The proposed adaptive law and controller successfully ensure FTHOS for DCRDNNs.
  • A specific case without external disturbances yields a corollary on FTOS.
  • A new adaptive scheme guarantees HOS in DCRDNNs with delayed couplings.
  • Simulation results validate the effectiveness of the developed synchronization criteria.

Conclusions:

  • The study provides effective solutions for finite-time synchronization problems in DCRDNNs.
  • Adaptive control strategies are robust to external disturbances and network delays.
  • The findings contribute to the theoretical understanding and practical application of synchronized neural networks.