Robust model-free formation control with prescribed performance and connectivity maintenance for nonlinear multi-agent systems

In this paper, we consider the formation control problem for a generic class of first-order nonlinear multi-agent systems, under an undirected communication model and connectivity constraints. More specifically, we design a decentralized model-free control protocol in the sense that each agent utilizes only local relative state information from its neighborhood set to calculate its own control signal, without incorporating any prior knowledge of the model nonlinearities/disturbances or any approximation structures to acquire such knowledge. Assuming that initially the graph is strongly connected, the proposed scheme guarantees that all initial communication links are maintained, that is all pairs of agents, initially forming an edge in the graph, remain within a distance representing the communication capabilities of the agents, preserving thus the strong connectiveness for all time. Additionally, the transient and steady state response is solely determined by certain designer-specified performance functions and is fully decoupled by the agents´ dynamic model, the underlying graph topology and the control gains selection, which further relaxes the control design procedure. Finally, the proposed methodology results in a low complexity design. Actually, it is a static scheme involving very few and simple calculations to output the control signal, thus making its distributed implementation straightforward.