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We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as an element in a reproducing kernel Hilbert space using a data-driven approach. Kernel methods provide a computationally efficient representation for the classifier that is the solution to a regularized least squares problem. The solution converges almost surely as the sample size increases, and admits known finite sample bounds. This approach is applicable to stochastic systems with arbitrary disturbances and neural network verification problems by treating the network as a dynamical system, or by considering neural network controllers as part of a closed-loop system. We present our technique on several examples, including a spacecraft rendezvous and docking problem, and two nonlinear system benchmarks with neural network controllers. 

In this paper an Unmanned Aerial Vehicles (UAVs) - enabled dynamic multi-target tracking and data collection framework is presented. Initially, a holistic reputation model is introduced to evaluate the targets' potential in offloading useful data to the UAVs. Based on this model, and taking into account UAVs and targets tracking and sensing characteristics, a dynamic intelligent matching between the UAVs and the targets is performed. In such a setting, the incentivization of the targets to perform the data offloading is based on an effort-based pricing that the UAVs offer to the targets. The emerging optimization problem towards determining each target's optimal amount of offloaded data and the corresponding effort-based price that the UAV offers to the target, is treated as a Stackelberg game between each target and the associated UAV. The properties of existence, uniqueness and convergence to the Stackelberg Equilibrium are proven. Detailed numerical results are presented highlighting the key operational features and the performance benefits of the proposed framework.