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

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.

I. Introduction

Consider a heterogeneous multi-agent system with one leader agent and follower agents. In the multi-agent system, different agents can have different dynamics. Each follower agent in the multi-agent system can access information from all its neighboring agents (that may include the leader agent as well). The leader agent has no neighbors. The information exchange among the agents is modeled via a communication graph. The output consensus problem for such a multi-agent system is to find a controller (for each follower agent) which, using the available information exchange, ensures that the output of each of the follower agents converges to the output of the leader agent. The output consensus problem for heterogeneous multi-agent system has been addressed by several works in literature that include [3], [6], [7], [9], [13], [16] and [19]. In [1] and [7], a leaderless output consensus problem has been solved for heterogeneous agents. While the controller in [1] has access to the state of its own agent and the relative state of each of the controller associated with its neighboring agents, the controller designed in [7] has access to its own state, the output of its own agent and output of the neighboring agents. In [7], a type generator is constructed along with a consensus controller for each of the agents such that the state of all the type generators achieve consensus, which is then used to drive the agents to output consensus. In [4] and [13] the output consensus problem is solved for heterogeneous leader-follower multi-agent system by designing a controller, for each of the follower agents, that requires the knowledge of the relative output of neighboring agents and the relative state of the controller associated with the neighboring agents. In [13], each follower agent can have unstable dynamics. First, using the knowledge of the state of the follower agent, each follower agent is stabilized via a controller and then a consensus controller is proposed using the solution of the regulator equations. The follower agent dynamics in [13] also contains a modified version of the output generated by the leader agent. Under the assumption that the transfer function of the linear system governing the agent dynamics has a particular structure, the output consensus problem for heterogeneous multi-agent system is solved in [15]. The proposed controller in [15] requires the knowledge of the relative output of its agent as well as the higher derivatives of the output for driving the agents to consensus. The work in [15] also considers unknown communication delays with a known upper bound. For first-order and second-order agent dynamics, a consensus problem is solved in [2] and [6] for heterogeneous agents. In [3], each of the follower agent is restricted to be minimum-phase and the dynamics of the leader agent is assumed to be embedded in the follower agent dynamics. All the follower agents in [3] can have different dynamics but must have the same relative degree. Under these assumptions, the output consensus problem is addressed in [3]. A linear matrix inequality based method is proposed in [19] to solve the leader-follower output consensus problem and a necessary and sufficient condition for output consensus of heterogeneous agents is presented in [16].