Control of acrobot based on Lyapunov function

Fuzzy control based on Lyapunov function was employed to control the posture and the energy of an acrobot to make the transition from upswing control to balance control smoothly and stably. First, a control law based on Lyapunov function was used to control the angle and the angular velocity of the second link towards zero when the energy of the acrobot reaches the potential energy at the unstable straight-up equilibrium position in the upswing process, The controller based on Lyapunov function makes the second link straighten nature relatively to the first link. At the same time, a fuzzy controller was designed to regulate the parameters of the upper control taw to keep the change of the energy of the acrobot to a minimum, so that the switching from upswing to balance can be property carried out and the acrobot can enter the balance quickly. The results of simulation show that the switching from upswing to balance can be completed smoothly, and the control effect of the acrobot is improved greatly.