Putting energy back in control

Energy is one of the fundamental concepts in scienceand engineering practice, where it is common to viewdynamical systems as energy-transformation devices. This perspective is particularly useful in studying complex nonlinear systems by decomposing them into simpler sub-systems which, upon interconnection, add up their energies to determine the full systems behavior. The action of a con-troller may be also understood in energy terms as another dynamical systemtypically implemented in a com-puterinterconnected with the process to modify its be-havior. The control problem can then be recast as finding a dynamical system and an interconnection pattern such that the overall energy function takes the desired form. This en-ergy shaping approach is the essence of passivity-based control (PBC), a controller design technique that is very well known in mechanical systems. Our objectives in this article are threefold