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This paper concerns with a new class of adaptive gain-scheduled H∞ control of linear parameter-varying (LPV) systems with nonlinear components. The plants considered are assumed to be polytopic LPV systems which have nonlinear elements, but the scheduled parameters and nonlinear elements in those plants are not known a priori, and thus, the conventional gain-scheduled control strategy cannot be applied. In the proposed adaptive schemes, the estimates of the scheduled parameters and nonlinear elements are obtained successively, and the current estimates are fed to the controllers to stabilize the plants and to attain H∞ control performance adaptively. The neural network approximators are introduced to obtain the estimates of the nonlinear elements, and the stabilizing signals are added to suppress the approximation errors and algorithmic errors included in the neural network structures. Those additional signals are derived from another H∞ control problem.