Controlling and Synchronization of Chaotic Systems Via Takagi-Sugeno Fuzzy Adaptive Feedback Control Techniques

In this research article, we have addressed the T-S (Takagi-Sugeno) fuzzy modeling and controlling and adaptive synchronization of chaotic systems. Based on the T-S fuzzy model, the fuzzy logic for controlling and synchronization for chaotic systems are designed via linear matrix inequality (LMI). We have illustrated the new chaotic Chen system. Lyapunov exponents and bifurcation diagrams of new Chen system are obtained to justify the chaos in system. Analytical and computational studies of new Chen systems with triangular fuzzy membership function have been performed by using LMI toolbox. Numerical simulation illustrates the controlling chaos as well as adaptive synchronization for the identical systems. Feedback gain matrices and Lyapunov positive definite matrix for the synchronization of identical new Chen systems are obtained.

Automated summary

This research article focuses on T-S fuzzy modeling, control, and adaptive synchronization of chaotic systems, using fuzzy logic and LMI. It introduces a new chaotic Chen system and conducts analytical and computational studies with triangular fuzzy membership functions. Numerical simulations demonstrate chaos control and adaptive synchronization for identical systems. Feedback gain matrices and Lyapunov positive definite matrix are obtained for synchronization of identical new Chen systems.