In this paper, we investigate affine formation control problem for a class of multi-agent systems (MASs) where the formation information is only accessible to a small group of agents. We propose a class of generic formation maneuver (GFM) functions and unified analysis method to study different convergence properties including finite-time, fixed-time and predefined-time strategy. We first propose a consensus-based formation control of leaders and then a stress-matrix-based formation control for followers. Different GFM functions are specified for finite-time, fixed-time and predefined-time formation control of leader and follower groups, respectively. Finally, a number of simulation examples are provided to prove the effectiveness of the proposed algorithm.