From the standpoint of inverse scattering theory, the problems of active control of sound can be interpreted as a special class of inverse source problems. We will describe an approach to obtaining general solutions of such problems for both continuous and discrete framework based on the theory of Calderon’s operators and the method of difference potentials by Ryaben’kii. We will also review a range of optimization formulations that arise naturally once the general solution has been built, and present the results of solving several specific optimization problems. Finally, we will describe a laboratory setting that has allowed us to corroborate the theoretical results experimentally.

Joint work with V. Ryaben’kii, J. Loncaric, S. Utyuzhnikov, A. Peterson, and others.