A new discrete mechanics approach to swing-up control of the cart-pendulum system

• A swing-up control method via discrete mechanics for the cart-pendulum is given.
• Theoretical analysis on the discrete cart-pendulum system is derived.
• The control method consists of the swing-up and stabilization stages.
• A transformation method from a discrete input to a continuous one is presented.
• Simulations show that the swing-up control is achieved by the new method.

This paper develops a new swing-up control method for the cart-pendulum system via discrete mechanics. The swing-up control law consists of two parts: the swing-up stage and the stabilization one. In the swing-up stage, we use a controller based on a discrete Lyapunov function and it can swing up the pendulum. Then, in the stabilization stage, we utilize a stabilizing controller based on the linearized system and discrete-time optimal regulator theory. In addition, transformation methods from discrete control inputs into continuous zero-order hold inputs are introduced. From some simulation results, we can confirm that the cart-pendulum system is swung up and stabilized by our new method.