Output consensus in a heterogeneous leader-follower multi-agent system with input and communication delays

Abstract

We consider the output consensus problem for a heterogeneous multi-agent system with one leader agent and $N$ follower agents. The dynamics of each follower agent is governed by a single-input single-output (SISO) stable linear system. The dynamics of the leader agent is governed by a marginally stable SISO linear system, input to which is zero at all times. Each follower agent has input and output delays which can be nonuniform across the multi-agent system. For each follower agent, we construct a pre-compensator and every follower agent has access to the output of the pre-compensator associated with its neighboring agents. A subset of the follower agents can also access the output of the leader agent. The communication delay, which is the delay in the exchange of outputs, is uniform across all the follower agents. All the delays present in the multi-agent system can be arbitrarily large but are known. For each pre-compensator, under the assumed information exchange, we design a feedback controller that drives the state of all the pre-compensators to a consensus trajectory. The synchronized outputs of the pre-compensators is then used to ensure output consensus among the follower agents. The controller design is robust to small perturbations in the communication delays. We demonstrate the efficacy of our design technique using a numerical example.