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Decentralized Diagnosis.

One common practical situation is that a DES is observed by multiple local sites with their own observation. In that case, it is desired that each failure is detected by at least one of the local sites such that the DES is co-diagnosable as defined in [D3]. In this context, the function IsCoDiagnosable verifies codiagnosability, while the function DecentralizedDiagnosers computes diagnosers that report failures at the different local sites. Finally, the function ModularDecentralizedDiagnoser computes decentralized diagnosers in the special case where the DES consists of multiple modular components, each corresponding to a local site.

Example

This example illustrates the usage of IsCoDiagnosable.

Consider the system G and the specification K in the figure below. We assume that there are two local sites with the observable events Sigma_1,o = {d,e,f,i} and Sigma_2,o = {d,h}. Then, it holds that the system is not diagnosable since the extensions of the failure string b cannot be distinguished from the extensions of the correct string a after the occurrence of a finite number of events due to the loop with the events e and f. Hence, IsCoDiagnosable returns a negative result.

Component G

Local specification K

On the contrary, IsCoDiagnosable returns a positive result for the next example with the system G, the specification K and the observable events Sigma_1,o = {d,i} and Sigma_2,o = {d,h}. In this case, the local site "1" can resolve the failure string b, while the local site "2" is able to detect the failure string c.

Component G

Local specification K

Example

The following figure shows the decentralized diagnosers for the previous example. In the case of the local site with the observation Sigma_1,o = {d,i}, the failure string b is uniquely identified after i occurs, while the second local site with the observation Sigma_2,o = {d,h} detects the failure c after the event h occurs.

Diagnoser for Sigma_1,o = {d,i} Diagnoser for Sigma_2,o = {d,h}

libFAUDES 2.32b --- 2024.03.08 --- with "synthesis-observer-diagnosis-iosystem-hiosys-multitasking-coordinationcontrol-timed-iodevice-simulator-luabindings"