Lyapunov´s stability control of constrained inverted pendulums

Control of a constrained planar inverted pendulum tracking desired trajectories is studied based on Lyapunov´s stability theory. The hinge at the base is replaced with horizontal and vertical forces. Two control strategies are designed: one is piecewise continuous which guarantees the Lyapunov´s stability; and the other one is continuous which is practically more desirable and can still keep tracking within prescribed accuracy. The trade-off in the stability using the continuous controller is analyzed. It is also found that the motion of the base point is significantly reduced as compared with previous work. The effectiveness of the controller is tested by computer simulation