Gradient-Descent based Nonlinear Model Predictive Control for Input-Affine Systems

This paper addresses the Nonlinear Model Predictive Control of Input-Affine Systems. The Two Point Boundary Value Problem resulting from the associated Optimal Control Problem is reformulated as an optimization problem, which is locally convex under assumptions coherent with the application. This optimization problem is solved on-line using the gradient descent method, where the gradients are approximated based on geometrical information of the dynamic system differential equations. The resulting control method is summarized in three algorithms. The proposed controller is easy to implement and requires no iterations. As a consequence, the suboptimal control input can be computed in a short time interval, making it ideal for fast highly nonlinear systems. As an example the attitude control of a quadrotor is presented. Simulation results show excellent performance in a wide range of state values, well beyond linear regimes.