Structural sliding equations for the tracking control of mechanical systems with active structure

The term of active structure is herein used (instead of variable structure) to emphasize that one deals with mechanical systems, some mechanical parameters of which (such as mass, inertia, rigidity) can be varied in time to account for environmental variations. One then has an internal structural control in addition to the usual external one in the form of forces or torques. By using a well-known classical result in physics, which characterizes a mechanical system by its Lagrangian only, one can obtain a new class of physically meaningful sliding equations for these systems. They are less severe regarding the mechanical constraints on the system, and they lower the amplitude of the chattering phenomenon. These systems can be controlled in a straightforward way by means of Barbashin-Utkin's variable structure technique.