Approximating Reachable Sets for Neural Network based Models in Real-Time via Optimal Control

In this paper, we present a data-driven framework for real-time estimation of reachable sets for control systems where the plant is modeled using neural networks (NNs). We utilize a running example of a quadrotor model that is learned using trajectory data via NNs. The NN learned offline, can be excited online to obtain linear approximations for reachability analysis. We use a dynamic mode decomposition based approach to obtain linear liftings of the NN model. The linear models thus obtained can utilize optimal control theory to obtain polytopic approximations to the reachable sets in real-time. The polytopic approximations can be tuned to arbitrary degrees of accuracy. The proposed framework can be extended to other nonlinear models that utilize NNs to estimate plant dynamics. We demonstrate the effectiveness of the proposed framework using an illustrative simulation of quadrotor dynamics.