A numerically stable constrained optimal filter design method for multichannel active noise control using dual conic formulation.

ABSTRACT

In practical active noise control (ANC) applications, various constraints are usually required, for example, the disturbance enhancement constraint, the robust stability constraint, and the controller output power constraint. One commonly used approach for designing a constrained ANC filter is to formulate a constrained optimization problem using an H / H framework, which requires significant computational power to solve. Recent work has shown that such an ANC filter design problem can be reformulated into a convex optimization problem and then further reformulated to a cone programming problem to reduce the required computational time by several orders. However, the standard cone programming reformulation procedure leads to a large number of free variables, which, in many applications, can adversely influence the numerical behavior of the optimization algorithm. In the current work, the ANC filter design problem structure is exploited in its dual conic form, which allows an elimination of free variables and can result in a numerically more stable solving process for the filter design problem while keeping the noise control performance unchanged. It is demonstrated that when compared with the reformulation using the standard procedure, the proposed formulation significantly improves its numerical stability and computational efficiency.