In many industrial and engineering applications, process control plays a central role. Among the possible control strategies, model predictive control (MPC), also called receding horizon control (RHC) , stands out for its excellent ability to handle constraints. While MPC has been successfully applied to many industrial applications, further developments are limited when it becomes necessary to solve many large on-line optimization problems. To overcome this situation, parametric optimization is often used such that most of the computation burden is pushed to an off-line phase. In this project, we propose to develop algorithms and software tools based on symbolic computation, to perform parametric optimization together with the corresponding on-line procedures, targeting MPC in the case of polynomial constraints and polynomial objective function . The proposed research will bring together the latest advances in computational real algebraic geometry and high-performance computing techniques.