Constrained optimal filter design for multi-channel active noise control via convex optimization.

Abstract

In many practical multi-channel active noise control (ANC) applications, various constraints need to be satisfied, such as stability, enhancement, etc. One way to enforce these constraints is to add a regularization term to the Wiener filter formulation, which, by tuning only a single parameter, can over satisfy many constraints and degrade the ANC performance. Another approach for non-adaptive ANC filter design that can produce better ANC performance is to directly solve the constrained optimization problem formulated based on the H2/H∞ control framework. However, such a formulation does not result in a convex optimization problem and its practicality can be limited by the significant computation time required in the solving process. In the presented work, the H2/H∞ formulation is convexified and a global minimum is guaranteed. It is then further reformulated into a cone programming problem which can be solved using specialized algorithms. Results show that the proposed method can produce better noise control performance than the regularization method. Compared with the traditional H2/H∞ formulation, the proposed method is more reliable and the computation time can be reduced by several orders, which, practically, provides a potential to extend its application to adaptive control.