Finite-Time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems with Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for non-strict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities. To eliminate nonlinearities, neural networks are applied to approximate the inherent dynamics of the system. In addition, due to the limitations of the actual working conditions, each follower agent can only obtain the locally measurable partial state information of the leader agent. To address this problem, a neural network state observer based on the leader state information is designed. Then, a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region, which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time. Finally, a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.