Warmstarting the constrained optimal filter design problem for active noise control systems in conic formulation

In practical active noise control (ANC) systems, constraints such as stability, need to be considered in the controller design process. The optimal control filters can be obtained by solving a constrained optimization problem, which requires a significant computational effort. Recently, a convex formulation in conic form was proposed for ANC applications which was shown to result in a computational time reduction by several orders. It is desirable to further improve its efficiency so that the optimal filter design process can be continuously repeated to achieve adaptive control for slow varying operating conditions. One potential way is to introduce a warmstart technique where the filter solution of a similar system or environment is used as the starting point of the optimization algorithm. However, the conic formulation should be solved by the interior-point method which, in general, is challenging for applying warm start techniques. In the current work, modifications are proposed to the original ANC filter design formulation so that the warmstart techniques can be applicable. The performance of warmstarting technique is investigated. Results show that an appropriate choice of warmstart strategy can significantly reduce the number of iterations required for solving the proposed conic formulation of ANC filter design problem.