On the design of linear time varying model predictive control for trajectory stabilization

Stabilizing a reference trajectory of a nonlinear system is a recurrent, non-trivial task in control engineering. A common approach is to linearize the dynamics along the trajectory, thus deriving a linear-time-varying (LTV) model, and to design a model predictive controller (MPC), which results to be computationally efficient, since only convex programs need to be solved in real time, while retaining constraint handling capabilities. Building on recent developments in gain-scheduling control design, where linearization errors and tracking error bounds are considered, a new approach to derive such LTV-MPC controllers is presented. The method addresses the systematic derivation of a suitable terminal cost. The resulting MPC law is tube-based, exploiting the co-designed auxiliary gain-scheduled controller. Computational and implementation aspects are discussed as well, and the resulting hierarchical method is demonstrated both in simulation and in experiments with a small drone with fast dynamics and limited embedded computational capacity.