This paper reports a flexible (or time-varying) multi-agent formation approach with average trajectory tracking for second-order integral multi-agent networks with single virtual leaders. The approach is developed by means of time-varying Olfati-Saber flocking algorithms, and sliding mode control (SMC) in terms of the leader-average dynamics. More precisely, SMC-specifying average trajectory tracking is combined with flexible multi-agent flocking driven by the Olfati-Saber flocking algorithms with timevarying weighting norm. Existence conditions and properties of the suggested multi-agent formation are examined rigorously, together with implementation formulas. It is shown that by designing the sliding surface and the time-varying weighting matrix appropriately, flexible formation with finite-time trajectory tracking can be achieved, free of control action chattering; moreover, the sliding mode control and formation control can be designed separately. Numerical examples are given to illustrate the main results. INDEX TERMS Multi-agent, flexible flocking formation, leader-average model, sliding mode control, trajectory tracking.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.