Active set vs. interior point strategies for model predictive control

We consider a comparison of active set vs. interior point strategies for the solution of receding time horizon problems in nonlinear model predictive control (NMPC). For this study we consider a control algorithm where we form quadratic programs (QPs) in each time horizon by linearizing the model. We also ignore second order information on the model and constraints. This approach can be viewed as a direct nonlinear extension of MPC with linear models and is easily tailored to include stabilizing constraints. Using this framework we consider the application of three active set strategies as well as interior point methods applied to both the NMPC and the QP subproblem. The first two active set methods (QPOPT and and QKWIK) are general purpose solvers that have been incorporated into SQP algorithms previously, while the third is a Schur complement approach that can easily exploit the sparse structure of the KKT matrix in MPC