Rigorous solution vs. fast update: Acceptable computational delay in NMPC

We present a method to improve the performance of nonlinear model predictive control (NMPC) by compromising between the time delay caused by a computational algorithm and the accuracy of the resulting control law in order to achieve best possible closed-loop performance. The main feature of the method is an a-priori error approximation derived for the neighboring-extremal update (NEU) algorithm, a fast NMPC algorithm presented recently by the authors. The error estimate provides the deviation of the current control trajectory from the (unknown) optimal control trajectory. The a-priori error estimator is incorporated in an on-line decision making process which simultaneously decides on the quality of the computed controls and the computational delay. In particular, the optimal number of QP iterations in an SQP strategy is determined on each horizon prior to the computation of the current control move.