Optimal control and synchronization of Lorenz system with complete unknown parameters

The paper discusses the optimal control and synchronization problems of Lorenz systems with fully unknown parameters. Based on the Liapunov–Bellman technique, the optimal control law with three-state variables feedback is derived such that the trajectory of the Lorenz system is optimally stabilized to an equilibrium point of the uncontrolled system. Further, another optimal control law is also applied to achieve the state synchronization of two identical Lorenz systems. Numerical results to demonstrate the effectiveness of the proposed control scheme.