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A learning approach for optimal feedback gains for nonlinear continuous timecontrol systems is proposed and analysed. The goal is to establish a rigorousframework for computing approximating optimal feedback gains using neuralnetworks. The approach rests on two main ingredients. First, an optimal controlformulation involving an ensemble of trajectories with 'control' variablesgiven by the feedback gain functions. Second, an approximation to the feedbackfunctions via realizations of neural networks. Based on universal approximationproperties we prove the existence and convergence of optimal stabilizing neuralnetwork feedback controllers.

Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation