A system for controlling an automotive or aircraft system or a physical plant using an embedded Model-Based Predictive Control controller by solving a quadratic programming optimization problem, the system comprising: an embedded platform comprising a model predictive control controller connected to a physical subsystem of the automotive or aircraft system; and wherein the MPC controller comprises: a state observer; and a semi-explicit quadratic programming solver connected to the state observer; and wherein the semi-explicit QP solver comprises: an optimization module; and a factorization module connected to the QP optimization module; and wherein the factorization module comprises: a memory having a saved factors unit; characterized by the following features: a factor search mechanism connected to the saved factors unit; and a factor update mechanism connected to the factor search mechanism; and wherein the factorization module provides variable ordering to reduce factors which need to be stored to allow them to be updated at a zero floating-point operations per unit time (FLOPs) cost. an embedded platform comprising a model predictive control controller connected to a physical subsystem of the automotive or aircraft system; and wherein the MPC controller comprises: a state observer; and a semi-explicit quadratic programming solver connected to the state observer; and wherein the semi-explicit QP solver comprises: an optimization module; and a factorization module connected to the QP optimization module; and wherein the factorization module comprises: a memory having a saved factors unit; characterized by the following features: a factor search mechanism connected to the saved factors unit; and a factor update mechanism connected to the factor search mechanism; and wherein the factorization module provides variable ordering to reduce factors which need to be stored to allow them to be updated at a zero floating-point operations per unit time (FLOPs) cost. a state observer; and a semi-explicit quadratic programming solver connected to the state observer; and wherein the semi-explicit QP solver comprises: an optimization module; and a factorization module connected to the QP optimization module; and wherein the factorization module comprises: a memory having a saved factors unit; characterized by the following features: a factor search mechanism connected to the saved factors unit; and a factor update mechanism connected to the factor search mechanism; and wherein the factorization module provides variable ordering to reduce factors which need to be stored to allow them to be updated at a zero floating-point operations per unit time (FLOPs) cost. an optimization module; and a factorization module connected to the QP optimization module; and wherein the factorization module comprises: a memory having a saved factors unit; characterized by the following features: a factor search mechanism connected to the saved factors unit; and a factor update mechanism connected to the factor search mechanism; and wherein the factorization module provides variable ordering to reduce factors which need to be stored to allow them to be updated at a zero floating-point operations per unit time (FLOPs) cost. a factor search mechanism connected to the saved factors unit; and a factor update mechanism connected to the factor search mechanism; and wherein the factorization module provides variable ordering to reduce factors which need to be stored to allow them to be updated at a zero floating-point operations per unit time (FLOPs) cost.