Fast Alternating Minimization Algorithm for Model Predictive Control

In this work, we apply the fast alternating minimization algorithm (FAMA) to model predictive control (MPC) problems with polytopic and second-order cone constraints. We present a splitting strategy, which speeds up FAMA by reducing each iteration to simple operations. We show that FAMA provides not only good performance for solving MPC problems when compared to other alternating direction methods, but also superior theoretical properties. Specifically, we derive complexity bounds on the number of iterations for both dual and primal variables, which are of particular relevance in the context of real-time MPC to bound the required online computation time. For MPC problems with polyhedral and ellipsoidal constraints, an off-line pre-conditioning method is presented to further improve the convergence speed of FAMA by decreasing the complexity upper-bounds and enlarging the step-size of the algorithm. Finally, we demonstrate the performance of FAMA compared to other alternating direction methods using a quadroter example.