Abstract
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.
Highlights
Miscellaneous systems can be modeled as multi-agent networks, while various control problems can be reformulated as formation manipulation of the dynamics and behaviours of the multi-agent networks
Multi-agent flocking strategies are adopted in autonomous unmanned vehicles as in [16], [48]; multi-agent collision control is exploited for power swing reduction and frequency synchronism in largescale power systems [51], [60]
We consider implementation of the time-varying flocking algorithm (5) while the average dynamics are tracking a specific trajectory via sliding mode control (SMC), which is induced by ur defined in (14), (15) and (17) as appropriately
Summary
Miscellaneous systems can be modeled as multi-agent networks, while various control problems can be reformulated as formation manipulation of the dynamics and behaviours of the multi-agent networks. To achieve flexible or time-varying multi-agent formation, interesting discussions are summarized in [1], [9], [10], [15], [50]. The generalized flocking algorithms of [31], [59] for the second-order integral multi-agent networks with single virtual leaders are further extended by employing time-varying weighting matrices in position and velocity metrics for flexible multi-agent formation control. Trajectory-tracking formation control is formulated and addressed in Section V with respect to the leader-average model. Let Mt =: M (t) ∈ Rn×n be a time-varying weighting matrix for inter-agent position difference metric in the Euclidean norm sense of.
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