Nonlinear MPC-Based Deep Neural Network for Chaotic System Synchronization

The synchronization of chaotic systems is a critical issue in nonlinear control theory, providing a foundation for various practical applications, such as fault detection, image encryption, and secure communication. However, chaotic systems are highly complex nonlinear dynamical systems. Therefore, achieving the required control accuracy of such systems represents a challenging task. In this paper, the nonlinear model predictive control (NMPC) methodology, combined with deep neural networks (DNNs), is applied for synchronization between master and slave chaotic systems. Such an approach aims to address the synchronization control problem under constraints, with an improved control performance and a minimal computational burden. An explicit NMPC controller is designed that is based on the idea to build offline a neural network approximation of the predictive controller. Then, online, the computation of control input consists of simple function evaluation as realized by the neural network. The performance of the NMPC-DNN is studied for third-order chaotic systems. The results show that the proposed control method leads to smaller synchronization error and stability of the master–slave chaotic systems.