A Study on Optimization Algorithms in MPC

We consider the implementation problem of Model Predictive Control (MPC) especially for linear control systems. In the real time computation of MPC, we need to choose an optimization method to solve at each sampling periods. For this purpose, we suggest a new combination of the existing numerical calculation methods to speed up the computer calculation. More precisely, we first introduce the well known KKT theorem in optimization problems, which is used in the MPC calculation procedure. Secondly, we review the MPC calculation and present a linear Lagrangian algorithm for the KKT theorem, which is combined with Wolfe conditions and Dual method. Finally, in order to demonstrate the proposed approach, we provide one numerical example and another example for stabilization of inverted pendulums.