Affine Formation Control of General Linear Multi-Agent Systems with Delays

This paper studies affine formation control problem of general linear multi-agent systems (MASs) over undirected graph in the presence of time delays. Different delay conditions are considered and predictive observers are designed for the followers to predict the states in the future. Then, affine formation control laws are designed based on the predicted states, and sufficient conditions are derived to ensure the convergence of the formation errors. With an adaptive mechanism, the proposed control laws can be implemented without the usage of global information. Under the proposed protocols, the MASs can form a target formation shape and realize time-varying geometric transformations continuously. Finally, simulations are conducted to verify the effectiveness of the theoretical results.