Improved stability conditions for unconstrained nonlinear model predictive control by using additional weighting terms

In this work, we present two unconstrained MPC schemes using additional weighting terms which allow to obtain improved stability conditions. First, we consider unconstrained MPC with general terminal cost functions. If the terminal cost is not a control Lyapunov function, but satisfies a relaxed condition, then our results yield improved estimates for a stabilizing prediction horizon. Furthermore, our analysis also allows to recover two well-known results as special cases: if the terminal cost function is chosen as zero, we recover previous conditions on the length of the prediction horizon such that stability is guaranteed; and if the terminal cost is a control Lyapunov function conform to the stage cost, stability follows independently of the length of the prediction horizon. Second, we propose to use an exponential weighting on the stage cost in order to improve the stability properties of the closed-loop. This also allows to consider local controllability assumptions in combination with a suitable terminal constraints and thereby gives a connection to the classical MPC approaches using terminal constraints.