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Detection and Identification of Abrupt Changes in Linear Systems

Linear, discrete-time, stochastic systems with parameters which may switch among a finite set of values are considered. The switchings are modeled by a semi-Markov, or a Markov, chain with known transition statistics. Abrupt changes in the system parameters may occur due to subsystem/component failures leading to structural changes, or due to system reconfiguration and repairs of the failed components, or due to changes in the environment in which the system must operate. The objective is to detect and identify the switchings in the parameters, given noisy measurements of the system output variables. The optimal solution is computationally demanding, therefore, suboptimal solutions are proposed. Simulation results are presented to illustrate the effectiveness of the proposed algorithms. It is also shown that the performance of the detector can be improved if a delay is introduced in processing of the measurements, i.e., if detection at time t is accomplished by using measurements till time t+N for some positive N.