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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 time-varying 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.

Multi-Agent Trajectory-Tracking Flexible Formation via Generalized Flocking and Leader-Average Sliding Mode Control