Discovering efficient periodic behaviors in mechanical systems via neural approximators

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of system. The classification geometric characterisation are in an on-going secular debate, recently led so-called eigenmanifold theory. characterises nonlinear oscillations as a generalisation linear eigenspaces. With motivation performing tasks efficiently, we use tools coming from this theory construct optimization problem aimed at inducing desired closed-loop through state feedback law. We solve constructed via gradient-descent methods involving neural networks. Extensive simulations show validity approach.