Reduced-order observer design for fault diagnosis of Boolean control networks

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In this paper, we propose an approach to design reduced-order observer of Boolean control networks (BCNs) for fault diagnosis by applying the semi-tensor product (STP) of matrices. At first, for observability analysis a computationally efficient approach based on the relational coarsest partition problem (RCP) is proposed. Then a necessary and sufficient condition for fault detectability analysis is introduced. After that an approach is introduced to design a reduced-order observer for fault detection. If fault occurrence has been detected, then an approach is proposed to solve fault isolation problem of BCNs. The basic idea is to separate dynamics of the faults into different independent subsystems by using graph theory. For each subsystem a residual generator is constructed based on reduced-order observer by getting rid of indistinguishable states. By theoretical analysis and simulation study it is shown that the approach proposed in the paper for fault isolation requires lower computational effort than the conventional scheme of a bank of full-order observers.