Constrained stabilization of a cart on an asymmetric-beam system through IDA-PBC

The problem of asymptotic stabilization of the cart on an asymmetric-beam system (CaB) is addressed and solved. This system captures the essential features of state-constrained stabilization while being underactuated. The control problem is solved through the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology. It is noticeable that considering the asymmetry of the beam makes the system quite challenging to be solved since, the solution with a constant inertia matrix reported so far is no longer valid. The performance of the control law is demonstrated through simulations.