The present work discusses a formulation for geometrically non-linear control of axial forces of stings in beam string structures. A tensegrity or cable net, which is stabilized by prestressing, is usually very deformable, and the governing eauations for these structures become highly geometrically nonlinear. In this paper, a method to determine the prestresses to be introduced in the stings is proposed based on Update Lagrangian Formulation for the prestressing to satisfy the conditions of constrains. Moreover, controllability of the non-linear control is discussed based on the controllability gramian matrix such as linear control. The determinant of the erramian matrix as performance criteria takes a minimum value when the matrix is singular. When the gramian matrix is non-singular, the system is controllable and the forces of actuators are determined by using minimum norm solutions of general simultaneous linear eauations. The availability of the present method is illustrated by the numerical study.
