Distributed Adaptive Time‐Varying Group Formation Tracking for Multiagent Systems With Input Saturation and Multiple Leaders of Unknown Input

ABSTRACT

In this article, we study a class of distributed adaptive time‐varying group formation tracking (TGFT) problems for linear multi‐agent systems (MASs) with multiple leaders under a directed topology, where the followers' inputs are subject to saturation and the leaders' control inputs are unknown. TGFT aims to drive followers to adjust their position states under the guidance of one or more leaders within each subgroup, thereby synchronously achieving the desired time‐varying sub‐formations. The leaders, whose control inputs are unknown, create non‐predictable and actionable trajectories. First, we thoroughly examine the TGFT problem and accomplish agent grouping by manipulating the properties of the Laplacian matrix. Subsequently, we propose a control protocol for group formation with multiple leaders. This protocol effectively accounts for the effects of unknown control inputs from the leaders, ensures efficient communication, establishes feasible constraints for formation tracking, and ultimately enables followers to successfully complete the desired formation tracking. Furthermore, we prove the stability of the multi‐agent system using the designed protocol constructed in this article, demonstrating that the general linear MAS can accomplish time‐varying formation tracking under saturated control inputs. Finally, we validate the theoretical results through numerical simulations, confirming the practical applicability of the proposed approach.