In this paper, we consider game problems played by (multi)-integrator agents, subject to external disturbances. We propose Nash equilibrium seeking dynamics based on gradientplay, augmented with a dynamic internal-model based component, which is a reduced-order observer of the disturbance. We consider single-, double-and extensions to multi-integrator agents, in a partial-information setting, where agents have only partial knowledge on the others' decisions over a network. The lack of global information is offset by each agent maintaining an estimate of the others' states, based on local communication with its neighbours. Each agent has an additional dynamic component that drives its estimates to the consensus subspace. In all cases, we show convergence to the Nash equilibrium irrespective of disturbances. Our proofs leverage input-to-state stability under strong monotonicity of the pseudo-gradient and Lipschitz continuity of the extended pseudo-gradient.
The leaching of ionic PAGs from model resist films into a static water volume is shown to follow first order kinetics. From the saturation concentration and the leaching time constant, the leaching rate at time zero is obtained which is a highly relevant parameter for evaluating lens contamination potential. The levels of leaching seen in the model resists generally exceed both static and ratebased dynamic leaching specifications. The dependence of leaching on anion structure shows that more hydrophobic anions have lower saturation concentration; however, the time constant of leaching increases with anion chain length. Thus in our model system, the initial leaching rates of nonaflate and PFOS anions are identical. Investigation of a water pre-rinse process unexpectedly showed that some PAG can still be leached from the surface although the pre-rinse times greatly exceeded the times required for saturation of the leaching phenomenon, which are expected to correspond to complete depletion of leachable PAG from the surface. A model is proposed to explain this phenomenon through re-organization of the surface as the surface energy changes during the air/water/air contact sequence of the pre-rinse process.
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