Synchronization of chaotic oscillator systems based on adaptive synergetic control theory

In this study, adaptive terminal convergence using robust synergetic control theory and finite-time attractor algorithms is explored to achieve synchronization and anti-synchronization between two different chaotic oscillator systems, while considering system uncertainties and external disturbances. To render the controller more robust and enable it to handle the nonlinear terms of the synchronized error system and to be easily implementable even when the bounds of system uncertainties and external disturbances are unknown, an adaptive control gain law derived from Lyapunov stability analysis is incorporated into the controller design. Numerical simulations are conducted to validate the proposed adaptive finite-time synergetic controller (AFSC) scheme. These simulations demonstrate that the AFSC outperforms the conventional adaptive synergetic controller (ASC) design by achieving more effective synchronization and anti-synchronization. The AFSC exhibits superior robustness, handling a wider range of system conditions and disturbances, making it practical for real-world scenarios where precise knowledge of system dynamics is often unavailable.