A system for embedding real-time Model Predictive Control (MPC) in a System-on-a-Chip (SoC) devices is provided. In the system, a microprocessor is connected to an auxiliary unit or application-specific matrix coprocessor. The microprocessor can control the operation of the MPC algorithm, i.e., carry out the tasks of input/output for the MPC algorithm, initialize and send the appropriate commands to auxiliary unit and receive back the optimal control moves or instructions from auxiliary unit. The auxiliary unit can operate as a matrix coprocessor by executing matrix operations, e.g. addition, multiplication, inversion, etc., required by the MPC algorithm.