Robust model predictive control for linear systems with constraints

The constraints make a process nonlinear even for a linear system in process control. A robust model predictive control (MPC) algorithm for the linear systems with disturbance by explicitly considering the constraints is proposed in this paper. By introducing an auxiliary system to the uncertain MPC system, the robust H₂ problem is converted to an LQ problem. Then the constraint can be exploited explicitly. Based on polynomial matrix description of the plant, the robust MPC algorithm is formulated as an optimization problem of a semi-definite programming. The utility of the proposed algorithm is demonstrated through a numerical example.