Minimum time trajectory optimization and learning

This paper presents a numerical algorithm for finding the bang-bang control input associated with the time optimal solution of a class of nonlinear dy namic systems. The proposed algorithm directly searches for the optimal swi tching instants based on a projected gradient optimization method. It is sh own that this algorithm can be made into a learning algorithm by using on-l ine 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 grad ients based on the theoretical state equation of the system but evaluated a long the actual state trajectory. The success of the method is demonstrated on an under-actuated double pendulum system called the acrobot.