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We study the effects of electron irradiation on suspended graphene monolayers and graphene supported on SiO2 substrates in the range 5.0 × 1015–4.3 × 1017 electrons/cm2. The suspended graphene monolayers are exfoliated over SiO2 substrates containing micrometer-sized holes, with graphene completely covering the hole, and are referred to as graphene drums. The irradiation was performed using a scanning electron microscope at 20–25 keV electron energy. We observe a two-stage behavior for the ID/IG, ID′/IG, and ID/ID′ ratios as a function of the average distance between defects, LD, where ID, IG, and ID′ are the intensities of the Raman D, G, and D′ peaks, respectively. Good fits to the dependence of the ratios on LD are obtained using the local activation model equation. The fits are used to characterize the defects at high defect densities. We also carried out annealing studies of samples irradiated to the first stage and used an Arrhenius plot to measure activation energies for defect healing, Ea. We measured Ea = 0.90 eV for the graphene drums, consistent with the hydroxyl groups; for supported graphene, we measured Ea = 0.36 eV, consistent with hydrogen adsorbates. We also studied the surface of the drums using atomic force microscopy and found no observable holes after irradiation and annealing. Our results show that the local activation model is useful in characterizing the defects in graphene drums. 

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-β activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.