Resilient consensus control for linear systems in a noisy environment

This paper presents multi-agent based control of networked systems in the presence of environmental noise. The subsystems are assumed to be linear time invariant with Gaussian white noise appearing as an exogenous input. The control protocol is based on output information received from other subsystems through the communication channel. We show that the multi-agent system arrives at a collective weak consensus in the sense that the sum of the mean square state errors between various subsystems converges to a small bound. Resilience is demonstrated in that the controller maintains collective stability in the event of communication or subsystem failures, with a degradation of performance. Simulation results are presented to illustrate the methodology.