Optimal feedback control of dynamical systems via value-function approximation

A self-learning approach for optimal feedback gains finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the value function obtained from a family of universal approximators. The cost functional training an approximate law incorporates two main features. First, it contains average over objective values parametrized ensemble initial values. Second, adapted exploit relationship between maximum principle dynamic programming. Based approximation properties, existence, convergence first order optimality conditions neural network controllers are proved.