Offline Robust Model Predictive Control for Lipschitz Non-Linear Systems Using Polyhedral Invariant Sets

In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.