Stability of Constrained Adaptive Model Predictive Control Algorithms
  Recently, suboptimality estimates for model predictive controllers (MPC) have been derived for the case without additional stabilizing endpoint constraints or a Lyapunov function type endpoint weight. The proposed methods yield a posteriori and a priori estimates of the degree of suboptimality with respect to the infinite horizon optimal control and can be evaluated at runtime of the MPC algorithm. Our aim is to design automatic adaptation strategies of the optimization horizon in order to guarantee stability and a predefined degree of suboptimality for the closed loop solution. Here, we present a stability proof for an arbitrary adaptation scheme and state a simple shortening and prolongation strategy which can be used for adapting the optimization horizon. 
Thomas Jahn and J\"urgen Pannek
math.OC cs.SY