A Linear Matrix Inequality (LMI) Approach to Robust Model Predictive Control (RMPC) Design in Nonlinear Uncertain Systems Subjected to Control Input Constraint

In this paper, a robust model predictive control (MPC) algorithm is addressed for nonlinear uncertain systems in presence of the control input constraint. For achieving this goal, firstly, the additive and polytopic uncertainties are formulated in the nonlinear uncertain systems. Then, the control policy can be demonstrated as a state feedback control law in order to minimize a given cost function at each known sample-time. Finally, the robust MPC problem would be translated into another optimization problem subjected to some linear matrix inequalities (LMI) constraints. The controller gains may be determined via the solution of the proposed minimization problem in a real-time way. The suggested method is numerically used in a second order nonlinear uncertain systems. The closed-loop performance would be compared with the other control techniques. The simulation results will show the effectiveness of the proposed algorithm in comparing with the existing control methods.