Oracle based approach to admissible invariant sets

Given a nonlinear system and a control law, a new method to obtain cutting planes excluding points not belonging to the maximal admissible invariant set is proposed. The method uses linearization along the trajectory of the close-loop system to obtain a set of cutting planes. The main advantage of the approach is that if an inner approximation of the maximal admissible invariant set is available, the provided cutting planes do not intersect this initial approximation. A scaled version of an initial invariant set is used to improve the cutting planes obtained by linearization. The proposed approach can be used in the context of nonlinear model predictive control. The method is illustrated by an example.