Distributed Average Tracking for Linear Heterogeneous Multi-Agent Systems with External Disturbances

In this paper, we address the distributed average tracking (DAT) problem for linear multi-agent systems with heterogeneous dynamics and external disturbances. The objective is that each agent can accurately track the desired tracking signal by designing controllers without initialization. The desired tracking signal means the average of individual time-varying reference inputs (one per agent). The current problem setting is technically more challenging and more practical than existing works. Based on the feedforward method, a state feedback controller is first designed to solve the DAT problem, which can guarantee the exponential convergence of tracking errors in the case where the desired tracking signal and external disturbances are known. Then the DAT problem for linear heterogeneous multi-agent systems with unknown desired tracking signal and unknown external disturbances is also solved. A distributed observer is designed for each agent to estimate the desired tracking signal. In parallel, the output of each agent is driven to track the output of the observer. Since each agent cannot access the desired tracking signal and external disturbances, a dynamic compensator independent of the exogenous signal and a dynamic internal-model based component are introduced to overcome these challenges. Finally, a numerical example is included for illustration.