Disturbance Decoupling and Instantaneous Fault Detection in Boolean Control Networks

Abstract

The literature available on disturbance decoupling (DD) of Boolean control network (BCN) is built on a restrictive notion of what constitutes as disturbance decoupling. The results available on necessary and sufficient conditions are of limited applicability because of their stringent requirements. This work tries to expand the notion of DD in BCN to incorporate a larger number of systems deemed unsuitable for DD. The methods available are further restrictive in the sense that system is forced to follow trajectory unaffected by the disturbances rather than decoupling disturbances while the system follows its natural course. Some sufficient conditions are provided under which the problem can be addressed. This work tries to establish the notion of disturbance decoupling via feedback control, analogous to the classical control theory. This approach though, is not limited to DD problems and can be extended to the general control problems of BCNs. Determination of observability, which is sufficient for the fault detection, is proven to be NP-hard for Boolean Control Network. Algorithms based on reconstructability, a necessary condition, of BCN turn out to be of exponential complexity in general. In such cases it makes sense to search for the availability of some special structure in BCN that could be utilized for fault detection with minimal computational efforts. An attempt is made to address this problem by introducing instantaneous fault detection (IFD) and providing necessary and sufficient conditions for the same. Later necessary and sufficient conditions are proposed for solving the problem of instantaneous fault detection along with disturbance decoupling using a single controller.