Recursively Feasible Model Predictive Control using Latent Force Models Applied to Disturbed Quadcopters

Abstract

In this work, recursively feasible model predictive control (MPC) is considered for systems under additive disturbances. Combining a nonparametric Gaussian Process (GP) prior for modeling the additive disturbance with the model of the undisturbed system results in a model structure referred to as latent force model (LFM). Using spectral factorization, the whole LFM can be represented by an equivalent/approximate stochastic state-space model used as the predictor in the MPC formulation. Chance constraints are incorporated by constraint tightening using so-called probabilistic reachable sets of the LFM state and recursive feasibility is guaranteed by optimizing the initial value of the MPC predicted trajectory. The LFM formulation allows leveraging the disturbance information to all components of the MPC, which can significantly enhance its performance. The proposed LFM-based MPC approach is demonstrated on a simulated quadcopter under additive disturbances. The performance of the closed-loop controller using the LFM-state-space reformulation is compared to standard MPC.