Decentralized adaptive formation control based on sliding mode strategy for a class of second-order nonlinear unknown dynamic multi-agent systems

This article investigates a decentralized adaptive sliding mode formation control (SMFC) based on the leader-follower formation strategy for a class of second-order nonlinear unknown dynamic multi-agent systems. Unlike the first-order multi-agent formation, the second-order formation needs to control not only the position but also the velocity, therefore it is more challenging and interesting. In order to handle the unknown dynamic problem, the adaptive neural network (NN) is employed to approximate the unknown dynamic function. Since every agent is required to directly communicate with leader agent, the adaptive NN law can be trained more sufficient. Moreover, in the control design, because a continuous proportional function is introduced to replace the discontinuous switching signal of the traditional sliding mode method, the chattering phenomenon that is a stubborn shortcoming of sliding strategy is effectively suppressed. According to Lyapunov stability analysis, it is proven that the proposed method can fulfill the control task. Finally, a numerical simulation example is executed to demonstrate the performance of the proposed controller.