Gradient-Based Model Predictive Control in a Pendulum System

Model predictive control (MPC) is applied to a physical pendulum system consisting of a pendulum and a cart. The objective of the MPC controller is to steer the system towards precomputed, time-optimal feedforward trajectories that move the system from one stationary point to another. The sample time of the controller sets hard limitations on the execution time of the optimization algorithm in the MPC controller. The MPC optimization problem is stated as a quadratic program, which is solved using the algorithm presented in [10]. The algorithm in [10] is an accelerated gradient method that is applied to solve a dual formulation of the MPC optimization problem. Experiments show that the optimization algorithm is efficient enough to be implemented in a real-time pendulum application