Stabilization of Underactuated Systems of Degree One via Neural Interconnection and Damping Assignment - Passivity Based Control

In this work, we show the potential of the universal approximation property of neural networks in the design of interconnection and damping assignment passivity-based controllers (IDA-PBC) for stabilizing nonlinear underactuated mechanical systems of degree one. Towards this end, we reformulate the IDA-PBC design methodology as a neural supervised learning problem that approximates the solution of the partial differential matching equations, which fulfills the equilibrium assignment and stability conditions. The output of the neural learning process has clear physical and control-theoretic interpretations in terms of energy, passivity and Lyapunov stability. The proposed approach is numerically evaluated in two well-known underactuated systems: the inverted pendulum on a cart and inertial wheel pendulum, whose analytic IDA-PBC solutions are non-trivial to obtain.