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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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Event-triggered protocol-based adaptive impulsive control for delayed chaotic neural networks.

Weilu Diao1, Wangli He1

  • 1Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai 200237, China.

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This study introduces adaptive impulsive control for synchronizing delayed chaotic neural networks. An event-triggered strategy ensures reliable synchronization without Zeno behavior, validated by an example.

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Area of Science:

  • Chaos theory
  • Neural networks
  • Control systems

Background:

  • Chaotic neural networks exhibit complex dynamics.
  • Synchronization of these networks is crucial for applications.
  • Delayed systems present unique control challenges.

Purpose of the Study:

  • To address the synchronization problem in delayed chaotic neural networks.
  • To design a flexible and effective adaptive impulsive control strategy.
  • To ensure the absence of Zeno behavior in the control system.

Main Methods:

  • Lyapunov-Razumikhin method for handling time delays.
  • Adaptive impulsive gain law design in a discrete-time framework.
  • Event-triggered impulsive strategy for control activation.

Main Results:

  • Criteria for guaranteeing synchronization of delayed chaotic neural networks are derived.
  • The proposed event-triggered impulsive strategy avoids Zeno behavior.
  • The adaptive impulsive control law is effective in achieving synchronization.

Conclusions:

  • The developed adaptive impulsive control strategy offers a robust solution for synchronizing delayed chaotic neural networks.
  • The event-triggered mechanism enhances control flexibility.
  • The findings are validated through a numerical example, demonstrating practical applicability.