Optimal diagnosis of changes in stochastic systems

The purpose of this paper is to give a statistical approach to the change diagnosis (detection/isolation) problem. The change detection problem has received extensive research attention. On the contrary, change isolation is mainly an unsolved problem. The author considers a stochastic dynamical system with abrupt changes and investigates the multihypothesis extension of Lorden´s results. The author introduces a joint criterion of optimality for the detection/isolation problem and then designs a change detection/isolation algorithm. The author also investigates the statistical properties of this algorithm. The author proves a lower bound for the criterion in a class of sequential change detection/isolation algorithms. It is shown that the proposed algorithm is asymptotically optimal in this class. The theoretical results are applied to the case of additive changes in linear stochastic models.