Abstract <p>The derivation of a differential equation for finding the control force when solving the generalized Chebyshev problem is presented in the paper; at the same time, the generalized Mei Fengxiang problem is formulated and solved. As an example of using the proposed theory, a practically important problem of suppression oscillations of a two-link manipulator “arm” is solved. The problem is solved by two completely different methods of control theory. In the first of them, the required horizontal force is found by one of the classical methods of control theory, which is Pontryagin’s maximum principle. It turns out that the resulting motion of the system has a remarkable property: throughout the entire motion, a linear eighth-order nonholonomic constraint constantly acts on the system! Therefore, the theory of motion for nonholomorphic systems with high-order constraints can be applied to solve the control problem. Such a theory was developed at the Department of Theoretical and Applied Mechanics of St. Petersburg State University. For this purpose, the control problem is formulated as a generalized Chebyshev problem, in which the solution to be found must satisfy not only the Lagrange equations, but also an additional linear high-order nonholonomic constraint with respect to highest derivatives. The generalized Gauss principle is used to solve the formulated generalized Chebyshev problem, and the new theory stated at the beginning of the paper is applied. The solutions obtained by both methods are compared, and the advantages of using the second method are explained.</p>