Modeling of Dynamical Systems via Successive Graph Approximations

Abstract A non-parametric technique for modeling of systems with unknown nonlinear Lipschitz dynamics is presented. The key idea is to successively utilize measurements to approximate the graph of the state-update function of the system dynamics using envelopes described by quadratic constraints. The proposed approach is then used for computing outer approximations of the state-update function using convex optimization. We highlight the efficacy of the proposed approach via a detailed numerical example.