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A constructive function approximation approach is proposed for adaptive learning control which handles finite interval tracking problems. Unlike the well established adaptive neural control which uses a fixed neural network structure as a complete system, in our method the function approximation network consists of a set of bases and the number of bases can be increased when learning repeats. The nature of basis allows the continuously adaptive tuning or learning of parameters when the network undergoes a structure change, consequently offers the flexibility in tuning the network structure. The expansibility of the basis ensures the function approximation accuracy, and removes the processes in pre-setting the network size. Two classes of system unknown nonlinear functions, either in L2(R) or a known upperbound, are taken into consideration. With the help of Lyapunov method, the existence of solution and the convergence property of the proposed adaptive learning control system, are analyzed rigorously.