Fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks
1School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.
Mathematical Biosciences and Engineering : MBE
|June 16, 2023
Summary
This study explores fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks. New conditions ensure stability and synchronization using a linear discontinuous controller.
Area of Science:
- Complex-valued neural networks
- Fractional-order systems
- Control theory
Background:
- Fractional-order systems offer enhanced modeling capabilities over integer-order systems.
- Complex-valued neural networks are crucial for processing complex data.
- Synchronization and stabilization are key challenges in neural network research.
Purpose of the Study:
- To investigate fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks with delays.
- To develop a linear discontinuous controller for achieving these objectives.
- To validate the proposed theoretical framework through simulations.
Main Methods:
- Application of fractional calculus principles.
- Utilizing fixed-deviation stability theory.
- Design and implementation of a linear discontinuous controller.
Main Results:
- Sufficient conditions derived for fixed-deviation stabilization.
- Sufficient conditions derived for fixed-deviation synchronization.
- Demonstration of controller effectiveness via two simulation examples.
Conclusions:
- The proposed method effectively achieves fixed-deviation stabilization and synchronization.
- The theoretical results are validated by simulation examples.
- The study contributes to the control of complex fractional-order neural networks.
Keywords:
discontinuous controlfixed-deviation dynamicsfractional-order complex-valued neural networkstime delaysMore Related Videos
11:54Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface
Published on: May 8, 2021
4.5K
09:01Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
Published on: April 4, 2017
8.7K
Related Concept Videos
01:21Linear Approximation in Time Domain
108
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,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
108
01:24BIBO stability of continuous and discrete -time systems
448
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....
448
01:07Time-Domain Interpretation of PD Control
147
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...
Consider the example of control of motor torque. Initially, a positive...
147
01:18Second Order systems II
137
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.
137
01:26Linear Approximation in Frequency Domain
117
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....
117
01:23Linear time-invariant Systems
298
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...
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...
298