Model Adjustable Predictive Control with Stability Guarantees

For stabilizing model predictive control adjusting the prediction model requires the adjustment of the terminal set and terminal cost. However, the conventional methods to design these are not practical, and often impossible, to implement in microcontrollers. In this paper, we pre-compute the terminal cost and terminal set in a form that allows to adjust them with minimal computational effort, following an adjustment of the prediction model. For unconstrained systems, a terminal cost and terminal controller are designed based on parameter-dependent Lyapunov functions. For constrained systems, the terminal function is also used to derive a robust polyhedral terminal set. We prove that the proposed method guarantees the existence of a terminal set with non-empty interior, and asymptotic stability of the closed-loop system.