Adaptive minimisation of the maximum error signal in an active control system

Most active noise control systems with multiple error sensors minimise the sum of the modulus squared outputs of these sensors. The purpose of this paper is to present an adaptive algorithm which minimises an alternative cost function which, in the limit, is equal to the maximum modulus squared value of all the error sensors. We investigate the physical consequences of minimise the maximum modulus squared output in this set to achieve noise reductions. The work is focused on an algorithm called the minimax algorithm. This algorithm has been studied in depth for an active control problem concerning one primary source, one secondary source and multiple error signals. The analysis covers steady state performance and convergence properties. In order to compare the proposed algorithm with the classical least squares solutions, a linear model of a one-dimensional acoustic system has been used, working at a single frequency.