Structural Exploitation for the Homogeneous Reformulation of Model Predictive Control Problems

Algorithms for solving Quadratic Programs (QPs) are indispensable in the research of Model Predictive Control (MPC) of linear dynamical systems. In a recent paper, Raghunathan [1] proposed a novel Homogeneous Quadratic Program (HQP) formulation that can determine optimality and infeasibility of QPs under assumptions that are readily satisfied for MPC. In this paper, we develop a structure exploiting factorization for the linear systems that occur when solving the QPs arising in MPC using the HQP formulation. We have developed a C++ framework (QOACH-MPC) that abstracts the structure exploiting factorization from the algorithm implementation, and makes it convenient for implementing and testing algorithms for MPC. Currently, QOACH-MPC implements an Interior Point Method (IPM) and Semismooth Newton Method (SNM) for solving the HQP, where the step computation exploits the structure in MPC. We demonstrate how our framework can be leveraged to produce a mixed algorithmic strategy for solving the closed-loop MPC problem.