The present thesis studies a strategy for the active non- linear control of dynamically loaded flexible structures. The control method is based on the non-linear optimal control theory using state feedback and the solution of the non-linear optimal control problem is obtained by representing system non-linearities and performance indices by power series with the help of algebraic tensor theory. General polynomial representations of the non-linear control law are obtained up to the fifth order. This methodology is applied to systems with quadratic and cubic nonlinearities, capable of representing most of the elements usually used in civil and mechanical engineering structures, such as beams, plates, shells and arcs. Control gains up to the third order are analytically derived and the effect of the control forces on the system is studied. Special emphasis is placed on systems susceptible to chaotic vibrations, escape from a potential well and dynamic jumps. Several examples are provided to illustrate the control approach. Strongly nonlinear systems subjected to free vibration, simple harmonic excitations, impact and ground acceleration are tested. The variation of the dynamic buckling load with the degree of the control algorithms is studied for the problem of structures with two potential wells, one of them corresponding to a post-buckling equilibrium position. The effect of time delay on controlled systems is studied analytically and numerically. The studied methodology is also applied to control the oscillations of simply supported buckled beams, in order to mitigate the effects of dynamic loading on the vibration amplitudes and prevent dangerous instability phenomena.