This paper presents a numerical algorithm for finding the bang-bang control input associated with the time optimal solution of a class of nonlinear dynamic systems. The proposed algorithm directly searches for the optimal switching instants based on a projected gradient optimization method. It is shown that this algorithm can be made into a learning algorithm by using on-line measurements of the state trajectory. The learning is shown to have the potential for significant robustness to mismatch between the model and the system. It learns a nearly optimal input through repeated trials in which it utilizes the measured terminal state error of the actual system and gradients based on the theoretical state equation of the system but evaluated along the actual state trajectory. The success of the method is demonstrated on an underactuated double pendulum system called the acrobot.

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