Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique.
Thierry Njougouo1, Victor Camargo2, Patrick Louodop1
1Research Unit Condensed Matter, Electronics and Signal Processing, University of Dschang, P.O. Box 67, Dschang, Cameroon.
Chaos (Woodbury, N.Y.)
|October 1, 2022
Summary
This study introduces optimal control for synchronizing Rössler chaotic oscillators in multilevel networks. The Hamilton-Jacobi-Bellman method ensures network synchronization, validated by simulations and experimental results.
Area of Science:
- Nonlinear Dynamics and Control Systems
- Chaos Theory Applications
- Networked Systems Synchronization
Background:
- Rössler chaotic oscillators are fundamental in studying complex dynamical systems.
- Synchronization in coupled chaotic oscillators is crucial for secure communication and signal processing.
- Multilevel network structures present unique challenges for control and synchronization.
Purpose of the Study:
- To design an optimal control strategy for synchronizing a multilevel network of Rössler chaotic oscillators.
- To ensure optimal synchronization of trajectories across all levels of the network.
- To validate the proposed control approach through numerical simulations and experimental correlation.
Main Methods:
- Application of the Hamilton-Jacobi-Bellman (HJB) technique for optimal control design.
- Development of a three-state variable feedback control law.
- Numerical simulations using MATLAB and circuit simulations using PSpice for validation.
Main Results:
- An optimal control law was successfully designed for multilevel Rössler chaotic oscillator networks.
- The proposed method achieved optimal synchronization of oscillator trajectories at each network level.
- Simulations demonstrated the effectiveness for single and triple network cases, with high correlation between MATLAB and PSpice results.
Conclusions:
- The Hamilton-Jacobi-Bellman technique provides an effective framework for optimal control and synchronization of chaotic oscillator networks.
- The designed controller is experimentally validated, confirming the theoretical findings.
- This work contributes to the advancement of synchronized chaotic systems and their practical applications.
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