First-order methods in embedded nonlinear model predictive control

Several algorithms based on Nesterov´s fast gradient method have been recently proposed in the literature for use in linear model predictive control (MPC). Their simple algorithmic schemes have attracted much attention for MPC applications on embedded hardware. The purpose of this paper is to investigate the suitability of these algorithms in a nonlinear MPC setup. We assess the necessary numerical modifications and analyze the additional online computational complexity. We illustrate our findings by combining different first-order methods with the real-time iteration (RTI) scheme for nonlinear MPC and using them to control a model of an inverted pendulum.