Dynamic systems satisfying the Dalembert-Lagrange principle are considered. The problem of control synthesis is posed as an inverse problem of dynamics, the solution of which is associated with a known problem. Its solution can be based on the reduction of the Lagrangian problem to the isoperimetric problem, which determines the purpose of the study. Since the procedure of reduction of the Lagrangian problem to the isoperimetric problem assumes various variants. It leads to the possibility of synthesizing quasi-optimal control laws and constructing control systems according to different criteria. Its realization leads to the derivation of the variational inequality. On its basis it is established that the synthesis of controls can be based on obtaining optimality conditions using constraints following from differential and integral variational principles. For this purpose, it is necessary to use constraints in the form of the Dalembert-Lagrange equation, Hamilton-Ostrogradsky action integral or Appel's acceleration energy when constructing the convolution of these expressions with the target functional. The considered problem of control synthesis is solved by applying the maximum principle of L.S. Pontryagin and the results of the Lagrange problem reduction to the isoperimetric problem. The practical significance of the obtained results is determined by the fact that the synthesis of controls using the reduction of the Lagrange problem to the isoperimetric problem does not require the resolution of the known problem of solving the two-point boundary value problem of the maximum principle of L.S. Pontryagin.