Learning-based parametrized model predictive control for trajectory tracking

This article is concerned with the tracking of nonequilibrium motions with model predictive control (MPC). It proposes to parametrize input and state trajectories of a dynamic system with basis functions to alleviate the computational burden in MPC. As a result of the parametrization, an optimization problem with fewer variables is obtained, and the memory requirements for storing the reference trajectories are reduced. The article also discusses the generation of feasible reference trajectories that account for the system's dynamics, as well as input and state constraints. In order to cope with repeatable disturbances, which may stem from unmodeled dynamics for example, an iterative learning procedure is included. The approach relies on a Kalman filter that identifies the repeatable disturbances based on previous trials. These are then included in the system's model available to the model predictive controller, which compensates them in subsequent trials. The proposed approach is evaluated on a quadcopter, whose task is to balance a pole, while flying a predefined trajectory.