Data Driven Verification of Positive Invariant Sets for Discrete, Nonlinear Systems

Invariant sets are essential when establishing safety of nonlinear systems. However, certifying the existence of a positive invariant set for a nonlinear model is difficult and often requires knowledge of the system's dynamic model. This paper presents a data driven method to certify a positive invariant set for an unknown, discrete, nonlinear system. A triangulation of a subset of the state space is used to query data points. Then, a convex optimization problem is used to create a continuous piecewise affine (CPA) function that fulfills the criteria of the Extended Invariant Set Principle by leveraging an inequality error bound that uses the system's Lipschitz constant. Numerical results demonstrate the program's ability to certify positive invariant sets from sampled data.