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

A learning approach for optimal feedback gains nonlinear continuous time control systems is proposed and analysed. The goal to establish a rigorous framework computing approximating using neural networks. rests on two main ingredients. First, an formulation involving ensemble of trajectories with ‘control’ variables given by the gain functions. Second, approximation functions via realizations Based universal properties we prove existence convergence stabilizing network controllers.