Distributed Consensus of Multi-agent Systems: An Integrated Adaptive Approach

An integrated adaptive protocols is proposed to solve the distributed consensus problem of multi-agent systems (MASs). In the existing adaptive consensus protocols, each agent is required to have a common and fixed control gain in the input matrix's column space. To expand the selection range of the control gain, this paper designs an integrated matrix-form adaptive protocol, where the control gain matrices can be adjusted adaptively by each agent according to the real-time consensus errors. The main difficulty of stability analysis lies in the nonlinear coupling in matrix form caused by the adaptive dynamics and the information interaction, which is overcome by constructing a trace-norm-based Lyapunov function. Moreover, the distributed integrated adaptive consensus protocol is extended to deal with the leader-follower consensus problem and the consensus problem with switching communication topologies. Numerical examples are presented to demonstrate that the proposed protocol is effective in certain cases where the existing ones fail.