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

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.