Asymptotic quickest change detection and isolation with polynomial delay penalties

In this paper, we consider the problem of quickly detecting and isolating an abrupt change in an observed stochastic processes under a polynomial penalty for delays. We propose an auxiliary matrix cumulative sum (AMCUSUM) detection and isolation algorithm, and show that it is optimal under our quickest change detection and isolation criterion with polynomial delay penalties in the asymptotic regime of few false alarms and false isolations. We also illustrate the AMCUSUM algorithm in simulations.