The problem is considered for control of an electromagnetic moment of the induction motor with a squirrel-cage rotor without the measurement of its rotational speed. By means of the principle of vector control, this problem reduces to developing an adaptive observer of values of the vector of the rotor magnetic-flux linkage. The method of recurrent objective inequalities (ROIs) is used, which enables one to reduce adaptation problems to counting systems of inequalities relative to the vector of the parameters estimated. For the control problem under consideration, these inequalities prove to be nonconvex, which makes it impossible to use directly the projection algorithms developed in the framework of the method of ROIs. In this connection, the common method for the stepwise reduction of the dimension of the nonlinear portion of inequalities is suggested in this work. On condition that the processes of a closed system display a certain natural property of nondegeneracy, this method permits reducing nonconvex inequalities to convex ones and ensures the achievement of the control aim on completion of the transient processes.