Towards Computationally Efficient NMPC Design with Stability Guarantee for Learning-Based Dynamic Models: A Case Study of UAVs

This paper proposes a novel computationally efficient nonlinear model predictive controller (NMPC) for learning-based models. The proposed NMPC scheme uses a hybrid model of the dynamic system, including a nominal derived model and a learning-based model that compensates for the incomplete knowledge of the system, i.e., unmodeled dynamics. The NMPC is designed with a tailored cost function that takes into account the learned-dynamics of the system. The cost function is formulated without stabilizing terminal conditions required for stabilization. Moreover, the proposed scheme facilitates the computation of the shortest possible stabilizing prediction horizon that guarantees the asymptotic stability of the closed-loop system. The proposed scheme is applied to an unmanned aerial vehicle (UAV) for validation. The performance of the proposed scheme is investigated through extensive numerical simulations and compared against the state-of-the-art traditional NMPC and traditional learning-based NMPC schemes proposed in literature. The results show superior trajectory tracking performance of the proposed learning-based NMPC scheme at short prediction horizons.