Abstract Adaptive dynamic programming (ADP) method can solve the problem of "curse of dimensionality" in the traditional dynamic programming, and has recently become a hot topic in the field of control theory and computational intelligence. For ADP method, a function approximation structure is used to estimate the performance index function, and then the approximate optimal control policy can be obtained based on the principle of optimality. As a kind of intelligent control methods with learning and optimization capabilities, ADP has great potential in solving the optimal control problem of complex nonlinear systems. This paper presents a comprehensive survey on the theoretical research, algorithm development, and related applications of ADP, which covers the latest research progress. It also analyzes and predicts the future development trend of ADP.

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