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This paper presents a nonlinear optimal control technique based on approximating the solution to the Hamilton-Jacobi-Bellman (HJB) equation. The HJB solution (value function) is approximated as the output of a radial basis function neural network (RBFNN) with unknown parameters (weights, centers, and widths) whose inputs are the system's states. The problem of solving the HJB equation is therefore converted to estimating the parameters of the RBFNN. The RBFNN's parameters estimation is then recognized as an associated state estimation problem. An adaptive extended Kalman filter (AEKF) algorithm is developed for estimating the associated states (parameters) of the RBFNN. Numerical examples illustrate the merits of the proposed approach.