On the Design of Terminal Ingredients for Linear Time Varying Model Predictive Control: Theory and Experimental Application

The use of Linear Time Varying (LTV) Model Predictive Control (MPC) to stabilize a set of trajectories of a nonlinear system is considered. This technique has been successfully applied in simulations and experiments, but only few contributions investigate stability aspects and the essential involved quantities: the terminal penalty and terminal constraint. Deriving the former is not always thoroughly addressed or it is based on the -rather restrictive- assumption that the whole set of linearized dynamics is quadratically stabilizable. In this article, we propose Linear Matrix Inequality (LMI) conditions to co-design a gain-scheduled auxiliary feedback and Lyapunov function, used to derive offline terminal set conditions and a terminal penalty constraint for an LTV MPC scheme guaranteeing stability and recursive constraint satisfaction. Recent results by the authors are extended to the case of a varying stage cost, such that the controller can be tuned to meet time-varying trade-offs between tracking accuracy and input activity. The approach is demonstrated in embedded hardware running on a CrazyFlie drone.