On approximate diagnosability of metric systems

The increasing complexity in nowadays engineered systems requires great attention to safety hazards and occurrence of faults, which must be readily detected to possibly restore nominal behavior of the system. The notion of diagnosability plays a key role in this regard, since it corresponds to the possibility of detecting within a finite delay if a fault, or in general a hazardous situation, did occur. In this paper the notion of approximate diagnosability is introduced and characterized for the general class of metric systems, that are typically used in the research community working on hybrid systems to study complex heterogeneous processes in cyber–physical systems. The notion of approximate diagnosability proposed captures the possibility of detecting faults on the basis of measurements corrupted by errors, always introduced by non-ideal sensors in a real environment. A characterization of approximate diagnosability in a set membership framework is provided and the computational complexity of the proposed algorithms analyzed. Then, relations are established between approximate diagnosability of a given metric system and approximate diagnosability of a system that approximately simulates the given one. Application of the proposed results to the study of approximate diagnosability for nonlinear systems, presenting an infinite number of states and of inputs, is finally discussed.