A game-theoretical perspective for decentralized active noise control

Active noise control (ANC) is a methodology that aims to attenuate acoustic noise creating a silent zone around the target. ANC techniques are particularly useful in the presence of low frequency noise, where passive control is ineffective and impractical. However, the computational cost of ANC applications involving a high number of sensors and actuators, such as active shielding, appears to be an important limitation. One possible approach to deal with this problem is to resort to decentralized control. This is a technique that decomposes a complex control problem into smaller ones that are addressed independently using different controllers. This article studies a decentralized scheme for ANC from a game-theoretical perspective. This formalizes the Nash equilibrium (i.e., the simultaneous best strategy) in the interaction between the controllers. Indeed, in the Nash Equilibrium, the control signals achieve stable conditions. In this framework, it is straightforward to analytically compare the decentralized control scheme to the standard centralized one.