Stochastic MPC with focus on probabilistic constraints with application to wind turbine control

The literature on stochastic MPC (SMPC) claims probabilistic constraints give a major feasibility problem and suggest solutions based on a combination of feedback and MPC. This paper explains it makes sense to relax the probabilistic constraints after the first part of the prediction horizon which solves the feasibility problem. Further, it is demonstrated that the effect that is special to probabilistic constraints is that they change the distribution of inputs and outputs. Current SMPC uses the conditional constraint probability given current measurements as the design parameter. Here a method to relate to the more application relevant unconditional constraint probability is developed. Finally, all the points are demonstrated with a simple wind turbine control problem which served as the motivation for this research in the first place.