A Linear Matrix Inequality Approach to Design Robust Model Predictive Control for Nonlinear Uncertain Systems Subject to Control Input Constraint

In this paper, a robust model predictive control (MPC) algorithm is designed for nonlinear uncertain systems in presence of the control input constraint. To achieve this goal, first, the additive and polytopic uncertainties are formulated in the nonlinear uncertain system. Then, the control policy is chosen as a state feedback control law in order to minimize a given cost function at each known sample-time. Finally, the robust MPC problem is transformed into another optimization problem subject to some linear matrix inequality (LMI) constraints. The controller gains are determined via the online solution of the proposed minimization problem in real-time. The suggested method is simulated for a second order nonlinear uncertain system. The closed-loop performance is compared to other control techniques. The simulation results show the effectiveness of the proposed algorithm compared to some existing control methods.