Adaptive Formation Control With Limited Information for Uncertain Nonlinear Multi-Agent Systems

The paper studies the distributed adaptive formation control in the setting of limited information transmitted between agents. The limited information, due to nonzero-kernel communication weight matrices between agents, has benefits in information security and privacy preserving, although as incomplete information, it challenges the formation control. Particularly, the multi-agent systems allow heterogeneous nonlinearities and serious uncertainties, making the formation control more difficult to achieve. In the paper, a fully-distributed adaptive control scheme is presented under appropriate conditions on the communication network, by incorporating two dynamic compensators and an auxiliary dynamic variable. The two compensators are employed to separately counteract the serious uncertainties and unavailable global information of the network resulting from unmatched states and weights. The auxiliary dynamic variable is introduced in the coordinate transformation to ensure the boundedness of the control, which cannot be derived by the traditional coordinate transformation. Two numerical examples are provided to show the effectiveness of the developed approach. Note to Practitioners—In real-world applications such as smart grids and smart transportation, communication networks play an essential role in cooperative operation, by which information is transmitted between agents. However, information transmitted in the communication network might be vulnerable to malicious eavesdropping due to the openness of networks. This could result in the leakage of sensitive information of agents, potentially disrupting the cooperative behavior and even the overall system security. In this paper, we consider adaptive formation control with limited information, instead of complete one. The limited information stems from nonzero-kernel weight matrices. In this case, even if the transmitted limited information is obtained by eavesdroppers, they still cannot reconstruct the full information of agents owning to the irreversibility of matrix weights, thus achieving information security and privacy preserving. In addition, the proposed distributed adaptive control strategy also can effectively counteract heterogeneous nonlinearities and serious uncertainties, which extends its application to a wide range of physical situations, such as cooperative engagement of multiple unmanned aerial and ground vehicles.