Control of acrobot based on non-smooth Lyapunov function and comprehensive stability analysis

A new control strategy for an acrobot based on a non-smooth Lyapunov function to guarantee the stability of the system in the whole motion space is presented. Three control laws are derived based on three Lyapunov functions and are applied successively in three stages of motion control to achieve a suitable posture and to increase the energy so as to make the acrobot move into the area around the unstable upright equilibrium position and to stabilise it at that position. These three Lyapunov functions are combined into one non-smooth function, which theoretically guarantees the stability of the acrobot in the whole motion space.