Direct Lyapunov approach for tracking control of underactuated mechanical systems

A direct Lyapunov method is applied to tracking problems for underactuated mechanical systems. The method involves reformulating the problem in terms of a sliding mode vector and then designing a control law that stabilizes the sliding mode vector to a lower bound. The design of the tracking control law utilizes the authors´ previous work on stabilization of underactuated mechanical systems using a direct Lyapunov method. One of the attractive features of the approach presented is that it requires no inverse dynamics. The efficacy of the method is demonstrated with applications to the ball and beam, where the unactuated axis is made to track a specified path, and to the inverted pendulum cart, where the actuated axis is made to track a specified path while maintaining stability of the pendulum.