The control problem for an underactuated Lagrangian system is considered. A system of smooth nonlinear functions of the generalized coordinates is introduced into the treatment and the number of functions is equal to the number of generalized control forces. The aim of the control is to bring the system in a finite time to a terminal set specified by the level lines of the selected functions, and it is required that the motion at the terminal instant occurs along the level lines. As a result, a development and extension of Chernous'ko's decomposition method is given. This method was proposed for designing feedback control for Lagrangian systems when the number of controls in a system is equal to the number of its degrees of freedom.
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