Section: New Results

Set theoretic fault detection and isolation

Participant : Sorin Olaru.

Fault-tolerant control theory is a well-studied topic but the use of the sets in detection, isolation and/or reconfiguration is rather tangential. Sorin Olaru together with his collaborators (and principally with F. Stoican) conducted a systematic analysis of the set-theoretic elements and devise approaches which exploit advanced elements within the field. The main idea is to translate fault detection and isolation conditions into those conditions involving sets. Furthermore, these are to be computed efficiently using positive invariance and reachability notions. Constraints imposed by exact fault control are used to define feasible references (which impose persistent excitation and, thus, non-convex feasible sets). Particular attention is given to the reciprocal influences between fault detection and isolation on the one hand, and control reconfiguration on the other. The recent results on this topic are gathered in the recent book [81] .

A new result has been obtained by the use of controlled invariance for the separation of faulty/healthy invariant sets in the detection and isolation [32] based on the necessary and sufficent conditions of George Bitsoris.

In a series of recent papers [67] , [68] , [70] , [69] , the link between the interval observers and the invariant sets have been investigated by establishing a series of formal results on the limit behaviour with potential applications in the detection and isolation of actuators faults