Controlling energy instead of position
Classic feedback control usually drives a system's position and velocity directly toward a target. For an underactuated system that approach often doesn't work near the state you actually care about, because there simply isn't enough direct control authority to push straight there. Energy-based control takes a different angle: instead of commanding position directly, it commands the total mechanical energy of the system, adding energy when there's too little and removing it when there's too much, using whatever actuation is available.
This matters because energy is a single scalar quantity that summarizes the whole state of a system like a pendulum, its height and speed together, and it can often be regulated with a comparatively simple control law even when position cannot be commanded directly. Once the system has the right amount of energy, a separate controller can take over to stabilize it precisely at the target state.