The fixed time dynamic compensation based prescribed performance formation control is developed for the position formation of heterogeneous multi-agent systems consisting of various unmanned aerial vehicles (UAVs) and unmanned surface vehicles (USVs). The prescribed performance formation control law is construed by introducing two flexible performance functions in terms of average and limit of the upper and lower flexible functions along the time axis. To estimate the uncertain dynamics of heterogeneous multi-agent systems, a fixed-time dynamic observer is designed. At the same time, a fixed time formation controller is designed with virtual speed controller. Through rigorous convergence analysis, the resulting fixed time formation law guarantees the desired formation position while the virtual velocity controller and fixed time dynamic observer are introduced. Finally, through the numerical simulation of the expected time-varying formation trajectory and the constant formation trajectory, the validity of the fixed-time formation controller with flexible prescribe performance.
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