Swarm Intelligence Approach for Controller Design Optimization Applied to Chaotic Synchronization of Continuous Dynamical Systems

Although the notion of chaos synchronization may seem counterintuitive at first sight, research has demonstrated that chaotic dynamical systems can indeed achieve asymptotic synchronization. A promising avenue in this area involves employing dynamic control mechanisms to compel the output signals of multiple chaotic systems to synchronize. Building upon this concept, this work presents a novel approach for designing a controller specifically tailored for synchronizing chaotic flows in a master-slave configuration. This process entails determining the optimal parameters of the controller, posing a challenging multimodal nonlinear continuous optimization problem. Our method relies on a powerful swarm intelligence technique called bat algorithm to tackle this issue. The performance of the method is assessed by its application to a master-slave couple of Duffing oscillators. Computational experiments demonstrate that the method exhibits notable performance in scenarios characterized by homogeneous driving, where it achieves perfect synchronization. However, it also shows limitations in scenarios featuring inhomogeneous driving.