Summary: How a network of multiple vehicles gets to a goal formation from an initial formation is as important as reaching the goal formation. Despite that stress matrix has been well applied to construct distributed affine formation control, most works have focused on the stabilization or stability issues and paid little attention to the performance regulation or the control parameterization issues. In this paper, we aim to design an error-model based distributed control for the affine formation maneuver of second-order multi-agent systems (MASs), and to demonstrate the advantages of the control approach in performance tuning. The basic idea behind the control design is to force the actual error-trajectory dynamics of each controlled follower to approximate that of an ideal second-order error model. The designed controller possesses a notable feature that the historical acceleration command (HAC) is used to enhance system performance during the formation maneuvers. By a theory tool of neutral functional differential equations, we develop a delay-independent condition on the design parameters, under which the system stability is robust to the actively introduced HAC. Furthermore, we derive an inequality describe the relationship between the ultimate bounds of tracking errors and the delay parameter. This paper presents a clear mechanism to tune the comprehensive performance of affine formation control. Simulation results show the effectiveness of the stability condition and the performance-tuning mechanism, as well as the possible fragility of the system stability to the delay when the condition is not satisfied.
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