Synchronization in a multilevel network using the Hamilton-Jacobi-Bellman (HJB) technique

TL;DR

This paper develops an optimal control method using the Hamilton-Jacobi-Bellman technique to synchronize multilevel networks of Rössler chaotic oscillators, validated through numerical simulations and experimental correlation.

Contribution

It introduces a novel HJB-based control law for multilevel oscillator networks, enabling optimal synchronization with experimental validation.

Findings

Successful synchronization of Rössler oscillators in simulations

Effective control law demonstrated for multiple network levels

Strong correlation between MATLAB and PSPICE results

Abstract

This paper presents the optimal control and synchronization problem of a multilevel network of R\"ossler chaotic oscillators. Using the Hamilton-Jacobi-Bellman (HJB) technique, the optimal control law with three-state variables feedback is designed such that the trajectories of all the R\"ossler oscillators in the network are optimally synchronized in each level. Furthermore, we provide numerical simulations to demonstrate the effectiveness of the proposed approach for the cases of one and three networks. A perfect correlation between the MATLAB and the PSPICE results was obtained, thus allowing the experimental validation of our designed controller and shows the effectiveness of the theoretical results.