Can we cope with the curse of dimensionality in optimal control by using neural approximators?

An approximation procedure termed "extended Ritz method" is presented for the solution of functional optimization problems. The properties of powerful nonlinear approximators, such as neural networks, are exploited to face highly nonlinear optimization problems in high-dimensional settings, with the possibility of avoiding the so-called "curse of dimensionality." As an example, a nonlinear control problem involving several tens of state variables is faced