A Modular Prescribed Performance Formation Control Scheme of a High-Order Multi-Agent System with a Finite-Time Extended State Observer

This paper proposes a modular control framework for high-order nonlinear multi-agent systems (MASs) to achieve distributed finite-time formation tracking with a prescribed performance. The design integrates two modules to address uncertainties and safety constraints simultaneously. Module I—Prescribed Performance-Based Trajectory Generation: A virtual signal generator constructs collision/connectivity-aware reference trajectories by encoding time-varying performance bounds into formation errors. It ensures network rigidity and optimal formation convergence through dynamic error transformation. Module II—Anti-disturbance Tracking Control: A finite-time extended state observer (FTESO) estimates and compensates for uncertainties within a finite time, while a time-varying surface controller drives tracking errors into predefined performance funnels. This module guarantees rapid error convergence without violating the transient constraints from Module I. The simulations verified the accelerated formation reconfiguration under disturbances, and thus, demonstrated improved robustness and convergence over asymptotic approaches. The framework offers a systematic solution for safety-critical MAS coordination with heterogeneous high-order dynamics.