Family of controllers for predefined-time synchronization of Lorenz-type systems and the Raspberry Pi-based implementation

In the context of different applications demanding fast, secure, and accurate chaotic systems synchronization, this article is concerned with improving the security and timeliness of chaotic synchronization schemes in chaotic secure information transmission. Firstly, we introduce five control laws designed to achieve predefinedtime chaotic synchronization within a master-slave scheme, employing a generalized Lorenz -type systems family as the chaotic model, guaranteeing that the chaotic systems achieve synchronization before a known predefined time. We apply the synchronization scheme in a practical application to validate its performance by implementing a secure communication system for image encryption on Raspberry Pi, using the MQTT protocol for transmission. We present system experimental results and evaluate its performance using diverse metrics, including errors, correlation, variance, and statistical tests like entropy, NPCR, and UACI.