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This paper introduces a provably stable adaptive learning controller which employs nonlinear function approximation with automatic growth of the learning network according to the nonlinearities and working domain of the control system. The unknown function in the dynamical system is approximated by piecewise linear models using the nonparametric regression technique. Local models are allocated as necessary and their parameters are optimized online. Inspired by composite adaptive control methods, the proposed learning adaptive control algorithm uses both the tracking error and the estimation error to update the parameters. We provide Lyapunov analyses that demonstrate the stability properties of the learning controller. Numerical simulations illustrate the rapid convergence of the tracking error and the automatic structure adaptation capability of the function approximator.