Tracking control of mechanical systems via sliding Lagrangian

According to a classical theorem in mathematical physics, a mechanical system is completely defined by its Lagrangian. This property is utilized to design the tracking control of manipulators via a new family of sliding surfaces referred to as ‘sliding Lagrangian surfaces’ and which exhibit some interesting features. They are physically meaningful. They create forces of reaction of low magnitude. They are intimately related to the second variation of the mechanical Lagrangian, in such a manner that one can refine the design by using a neighbouring-optimal control involving linear dynamic and quadratic cost. One can also combine the approach with the variable structure technique to achieve a good robustness with a low chattering phenomenon.