Tailored QP algorithm for Predictive Control with dynamics penalty

In order to reduce the computational complexity of solving Quadratic Programming (QP), related to linear Model Predictive Control (MPC), a new approximated formulation of the QP with simple bounds is introduced in this paper. This formulation is based on the idea not to consider model dynamics as a hard constraint but rather modify the objective function of MPC by penalty to capture the violation of model dynamics. The system dynamics is usually uncertain and then it does not make sense to design the control law based on the exact model. Furthermore, the specific sparse structure of the approximated simple bounded QP formulation of the MPC problem is exploited in the new type of combined gradient/Newton step projection algorithm with linear complexity of each iteration with respect to prediction horizon. It is shown by examples that the proposed method is faster on tested problem than other state-of-the-art solvers while retaining a high performance level.