Dominating neighbourhood observers for fault reconstruction

In this paper, semi-decentralized sliding mode observers are designed for a network of homogeneous linear time invariant dynamical systems, represented in terms of a graph based on relative information. The proposed sliding mode observers reconstruct actuator faults occurring at the node itself as well as in the closed neighbourhood node set. Two distinct observer frameworks are proposed. In the first one, observers are deployed at every node, whereas in the second framework, the observers are placed only on nodes which define the dominating node set. Minimizing the number of observers required, while providing complete monitoring coverage across the network, is the key advantage of the latter framework. The methodology is demonstrated using a formation flying scenario involving a network of ten satellites. Semi-decentralized super-twisting sliding mode observers have been designed to circumvent issues associated with fault reconstruction when only the relative positions of the satellites are assumed to be available for monitoring purposes.