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The paper focuses on a direct adaptive control plant developed for highly uncertain nonlinear systems, that does not rely on state estimation. In particular, we consider single-input/single-output nonlinear system, whose output has known, but otherwise arbitrary relative degree. This includes systems with both parameter uncertainty and unmodeled dynamics. The result is achieved by extending the universal function approximation property of parameterized neural networks to model unknown system dynamics from input/output data. The network weight adaptation rule is derived from Lyapunov function analysis, and guarantees that the adapted weight errors and the tracking error are bounded. Based on the design of adaptive neural network control, a practical application to the Vibroseis system has been achieved.