  A discrete time control algorithm using the damped least squares is
introduced for acceleration and energy exchange controls in nonlinear vibrating
systems. It is shown that the damping constant of least squares and sampling
time step of the controller must be inversely related to insure that vanishing
the time step has little effect on the results. The algorithm is illustrated on
two linearly coupled Duffing oscillators near the 1:1 internal resonance. In
particular, it is shown that varying the dissipation ratio of one of the two
oscillators can significantly suppress the nonlinear beat phenomenon.
