The purpose of this paper is to analyze the problem of controlling the plane-parallel motion of a circular foil in an ideal fluid by changing the intensity of attached sources and rotation of the internal rotor.

Methods. To develop the mathematical model, use is made of the description of fluid motion based on a complex potential, which allows calculation of the fluid forces acting on the moving body. To solve the control problem, the assumption of the piecewise constant
form of control actions is made, which allows the equations of motion to be explicitly integrated by analytical methods.

Results. Equations of the plane-parallel motion of a circular (generally unbalanced) foil with an arbitrary number of attached sources are derived. The motion of the sources relative to the foil and their intensities are given by explicit functions of time. An explicit integration of the equations of motion is performed for the case of a balanced foil with one attached source for piecewise constant controls.

Conclusion. Explicit solutions to the equations of motion are used to design gaits for in-place turning and forward movement. An algorithm for moving the foil in the neighborhood of a prescribed trajectory by alternately using elementary gaits is formulated. The proposed algorithm of trajectory control is a constructive proof of the controllability of the system considered. The solution to the control problem obtained in this way can be used as a basis for solving the same problem in the case of smooth controls.