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This article studies the adaptive optimal control problem for continuous-time nonlinear systems described by differential equations. A key strategy is to exploit the value iteration (VI) method proposed initially by Bellman in 1957 as a fundamental tool to solve dynamic programming problems. However, previous VI methods are all exclusively devoted to the Markov decision processes and discrete-time dynamical systems. In this article, we aim to fill up the gap by developing a new continuous-time VI method that will be appli
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