Consensus of First Order Multi-agent Systems with Actuator or dynamic Fault by weighted adjacency matrix approach (WAMA)

In this paper, the consensus problem for the first-order discrete-time multi-agent systems (MASs) In the presence of fault is studied. This study uses two concepts of watchdog model-based observer and weighted adjacency matrix approach (WAMA). The purpose of this study is to reach a consensus on MASs when one or more agents have been damaged. In this method, for any agent, a watchdog that measures the amount of difference between the states of the actual system and the calculated states of the system by the agent's model is designed, this generated residual declares the amount of agents deviation. A decision function is used to decide how this malfunctioning affects the neighboring agents. Therefore, the states that each agent transmits to the neighboring agents are augmented by the output of the decision function. By increasing states matrix dimensions, each agent will report its health status or commanding by using a new state to the neighboring agents. This additional state is affected by a decision function that expresses the neighboring agents how should behave with this malfunction agent. Finally, the produced residue will be weight of the adjacency matrix and will cause to correct consensus. Simulation results are presented to illustrate the effectiveness of this approach.