Reinforcement learning has been applied with remarkable sucess in some classical control problems [1]. While this seems to indicate a good potential for more applications it is still important to look at these problems from a classic perspective to: first, have a strong understanding of how the field developed and, second, to have a broad palette of solutions.

One such problem is the so called Inverted Pendulum Swing-up problem. This problem's objective is to balance a pendulum in an upright position starting from a resting position, as can be seen in this demonstration video from the University of São Paulo:

Vid. 1 - Inverted Pendulum Swingup

In this article we will go over all the steps required to solve this problem with the Model Predictive Control (MPC) framework:

  1. Mathematically modelling the systems dynamics using the Lagrangian method.
  2. Problem formulation in an optimization setting, defining the cost function and constraints.
  3. Optimization solving the problem numerically.

1. Mthemtic Moe


Fig. 1 - Inverted Pendulum