A Predefined-Time Approximate-Convergence Neural Dynamics Controller for Function Projective Lag Synchronization of Complex-Valued Chaotic Systems and Its Application

The nonlinear behavior with unpredicted property in engineering has received widespread attention. To explore more unpredicted nonlinear behavior, this paper focuses on the function projective lag synchronization (FPLS) of complex-valued chaotic systems. Most existing control schemes primarily address system stability, lack of consideration in convergence improvement. Zeroing neural dynamics (ZND) has significant results in the convergence performance, yet achieving a balance between model structure and performance remains a challenging task. In light of this, we propose a general time base generator (TBG), and adopt the linear ZND with the simplest structure, which has relatively weak convergence but devoid of nonlinear components, to develop a TBG based neural dynamics controller (TBGBNDC) in the FPLS of complex-valued chaotic systems. The theories illustrate that the system error under the TBGBNDC has predefined-time asymptotic convergence, which is verified in both homogeneous and heterogeneous complex-valued chaotic systems. Compared with other controllers, the TBGBNDC exhibits better performance in terms of convergence, energy and time consumption. Furthermore, the higher-quality random sequences are acquired through the FPLS between these chaotic systems, showing the significant potential application of the research topic.