Fully distributed finite‐time consensus under state‐dependent communication network

Abstract Network topology is one of crucial components in multi‐agent systems, and it reflects the information interaction between agents. In many practical multi‐agent systems, for example, wireless sensor networks, the interactions between agents can be characterized by a state‐dependent graph, in which the weights vary with the relative agent states. How to achieve the finite‐time consensus under the state‐dependent graph is worth in‐depth research and especially integrates/reforms the relevant techniques. This paper addresses the finite‐time consensus for uncertain nonlinear multi‐agent systems under a state‐dependent graph. Typically, the systems allow severe uncertainties in control coefficients and nonlinearities, which, together with the state‐dependent graph, renders the protocol design of finite‐time consensus more difficult. To this end, a fully distributed protocol with dynamic high gain is designed. Notably, in the protocol, only one dynamic high gain, rather than multiple ones in related existing results, is sufficient to deal with the uncertainties and the unavailable global graph information. Especially, a condition which relies on the specified distance and the system initial states is presented to guarantee the connectivity of the graph. It turns out that by the protocol and condition, the finite‐time consensus is achieved. Simulation results are given to illustrate the validity of the proposed method.