Active fault detection and control: Unified formulation and optimal design

A new unified formulation of the active fault detection and control problem for discrete-time stochastic systems and its optimal solution are proposed. The problem formulation stems from the optimal stochastic control problem and includes important special cases: an active detector and controller, an active detector and input signal generator, and an active detector with a given input signal generator. The optimal solution is derived using the so-called closed loop information processing strategy. This strategy respects the influence of the current decision and/or input on the future behavior of the observed system, allows penalizing future wrong decisions, and improves the quality of fault detection. The proposed formulation and obtained solution also provide better understanding of the active fault detection and its relation to the optimal stochastic control. The results are illustrated in numerical examples.