Observer-Based Stipulated-Time Formation Tracking of Switching Multi-Agent Systems With Adjustable Transient Behavior

This paper investigates the distributed stipulated-time formation tracking problem for second-order multi-agent systems (MASs) under both fixed and switching communication topologies. In contrast to existing predefined-time and prescribed-time approaches that only guarantee convergence within a conservative upper bound, the proposed method enables the exact settling time of both estimation and tracking errors to be explicitly assigned, independent of initial conditions. Improved stipulated-time distributed observers are developed for both scenarios, where a single design parameter can directly preassign the actual convergence time. Based on the observer design, an observer-based formation control framework is constructed to ensure that all agents achieve the desired formation precisely at the specified time. Furthermore, a class of time-varying regulation functions is incorporated into the control design to explicitly shape the transient behavior while avoiding excessively large control gains, thereby enhancing practical applicability. Theoretical analysis, along with numerical simulations and physical experiments, validates the effectiveness and robustness of the proposed approach. Overall, the proposed framework provides improved temporal accuracy, enhanced transient flexibility, and better practical performance compared with existing prescribed-time methods.