Global natural /spl theta/-tracking control of Lagrangian systems

The Lagrange differential equation is used in its general vector form without any information either about system parameters and nonlinearities or about external disturbances so that their real forms and values are allowed to be completely unknown. A demanded system global tracking quality is defined by a vector differential equation in terms of the error vector of the general coordinate vector /spl theta/. In order for a tracking control to exist for such a system and under such a lack of information, the system should obey a qualitative dynamical property, called the global natural /spl theta/-trackability. The necessary and sufficient conditions for global natural /spl theta/-trackability are presented. They compose a part of the whole set of the necessary and sufficient conditions for a control to be global natural /spl theta/-tracking control of the system, which guarantees the requested tracking quality. The paper results are based on new issues in the framework of the Lagrangian systems such as the physical continuity and uniqueness principle.