A new strategy based on the direct use of strain sensing is proposed for the minimization of the acoustic radiation from a vibrating plate. This strategy uses active structural acoustic control because it eliminates the need for far-field acoustic sensors. The cost function is defined as the radiated acoustic power and the discrete strain information is given directly, for example, by fiber optic sensors embedded in the structure. Two approaches are presented to express the cost function in terms of strain information. The first one is based on plate’s displacement reconstruction from the strain field while the second is based on integration by parts of the wave-number transform of the displacement. Proper concentration of the control effort is obtained with the cost function defined in the wave-number domain. Both approaches are first validated with respect to an analytical solution for the calculation of the radiated acoustic power from structural strain information. It is shown that good agreement is obtained with at least two strain sensors per structural wavelength. Optimal control of acoustic radiation from a simply supported plate is then performed using different configurations of sensors and actuators. The control is performed using simulated piezoelectric actuators and results show that both approaches are well suited for active control applications as they offer good performance over a wide frequency range while requiring only few sensors.