Virtual Actuator and Sensor Fault Tolerant Consensus for Homogeneous Linear Multi-Agent Systems

This paper presents a fault tolerant consensus protocol for homogeneous linear multi-agent systems using virtual actuators and virtual sensors. By means of the virtual actuators/sensors, the faulty system is reconfigured so that it can be brought into a block-triangular form through an appropriate change of variables. In this way, a Lyapunov-based approach can be used to obtain design conditions expressed as a feasibility problem involving linear matrix inequalities (LMIs). Both the linear time invariant (LTI) and the linear parameter varying (LPV) cases are discussed, the latter under the assumption of synchronized trajectories of the time-varying parameters. An academic example is used to illustrate the main features of the proposed fault tolerant consensus protocol. In particular, it is shown that by activating the virtual actuators/sensors, the agents achieve consensus in spite of severe faults, whereas instability of the synchronization errors occurs if no fault tolerant strategy is employed.