Adaptive control and synchronization of Lorenz systems

This study addresses the adaptive control and synchronization problems of Lorenz systems with unknown system parameters. Based on the Lyapunov stability theory, an adaptive control law with single-state variable feedback is derived such that the trajectory of the Lorenz system is globally stabilized to an equilibrium point of the uncontrolled system. In addition, the adaptive control law is also applied to achieve the state synchronization of two identical Lorenz systems. Numerical results demonstrate the effectiveness of the proposed control scheme.