Adaptive algorithms for underdetermined active control problems

In active sound control, the sound field generated by the operation of a number of secondary actuators is adjusted to destructively interfere, to the greatest possible extent, with the sound field caused by the original, primary, source of sound. An example would be the adjustment of the inputs to structural actuators attached to a panel, also excited by a primary source of vibration, to minimize the acoustic power radiated. In practice the inputs to a number of actuators could be adjusted to minimize the sum of the squared signals from a greater number of sensors-an overdetermined control problem, for which adaptive algorithms have already been developed. An alternative control strategy is to adjust the actuators so that the signal from a single sensor, such as one measuring the net volume velocity of a panel, is driven to zero with the least control effort. Adaptive algorithms for such underdetermined control problems are discussed.<>