Active set prediction for nonlinear model predictive control on a shrinking horizon based on the principle of optimality

We provide insights into the structure of the set of active constraints arising for optimal solutions to nonlinear model predictive control problems along a shrinking horizon. The principle of optimality combined with a particular order of the constraints allows the prediction of the future active sets without solving the corresponding optimization problem. By describing the development of optimal active sets along a shrinking horizon, we state an important relationship for transferring ideas such as dynamic programming approaches from the linear to the nonlinear case. We further use the information about active and inactive constraints to rearrange and remove constraints of the original nonlinear program as described in previous work and thus simplify the problem. Numerical experiments show for the problem class treated here that the inherent robustness coming with the regional characteristic of the active sets with respect to the state space makes this approach useful also if uncertainties are present.