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In this paper, we study the problem of distributed generalized stochastic Nash equilibrium seeking for robot systems over a connected undirected graph. We use the cost functions containing uncertainty to represent the system’s performance under varying conditions. To mitigate the challenges posed by this uncertainty, we employ the Tikhonov regularization scheme, which also helps us to relax the strongly monotone condition of the cost functions to the strictly monotone condition. We also consider the inequality constraints, which represent the feasible working space of robots. Additionally, auxiliary parameters are introduced in the control laws to facilitate seeing the variational generalized stochastic Nash equilibrium. The convergence of the proposed control laws is analyzed by using the operator splitting method. Finally, we demonstrate the effectiveness of the proposed algorithm through an example involving multiple robots connected through a communication network. 

Within the cuprate constellation, one fixed star has been the superconducting dome in the quantum phase diagram of transition temperature vs. the excess charge on the Cu in the CuO2-planes, p, resulting from O-doping or cation substitution. However, a more extensive search of the literature shows that the loss of the superconductivity in favor of a normal Fermi liquid on the overdoped side should not be assumed. Many experimental results from cuprates prepared by high-pressure oxygenation show Tc converging to a fixed value or continuing to slowly increase past the upper limit of the dome of p = 0.26–0.27, up to the maximum amounts of excess oxygen corresponding to p values of 0.3 to > 0.6. These reports have been met with disinterest or disregard. Our review shows that dome-breaking trends for Tc are, in fact, the result of careful, accurate experimental work on a large number of compounds. This behavior most likely mandates a revision of the theoretical basis for high-temperature superconductivity. That excess O atoms located in specific, metastable sites in the crystal, attainable only with extreme O chemical activity under HPO conditions, cause such a radical extension of the superconductivity points to a much more substantial role for the lattice in terms of internal chemistry and bonding.