Lag formation control in distributed multi‐agent system with neural networks and sliding mode strategies

The distributed lag formation approach enhances robustness and scalability by enabling followers in high‐order multi‐agent systems to estimate and track the leader's state under unknown dynamics and bounded disturbances, eliminating the reliance on centralized information. To solve the leader‐following lag formation problem in high‐order multi‐agent systems in unknown dynamic and bounded disturbances scenario, we propose a distributed lag formation approach which leverages neural network systems and second‐order sliding mode control, where the neural network serves to approximate unknown dynamics, and its approximation errors and external disturbances are mitigated through continuous second‐order sliding mode control. The proposed controllers ensure that all followers' outputs can effectively track those of the leader. Utilizing Lyapunov stability theory, we prove that global tracking errors can converge to a small neighborhood around the origin. Simulation examples demonstrate that the efficacy of our proposed lag formation scheme.