Abstract
Time delay phenomenon of nonlinear system is the objective phenomenon exists in nature. Because the control inputs also contain time delays, the presence of the time delay makes the system current input and time delay input exist coupling. The derivative of the performance index function can not be directly derived display expressions of optimal control. Using the adaptive dynamic programming (ADP) iterative algorithm to solve time delay equation, and the convergence proof is given. The optimal control law of the system can be obtained by the performance index function approximate solution.
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