Stochastic Consensus Control Integrated With Performance Improvement: A Consensus Region-Based Approach

The randomly switching communication topologies are of particular interest for researchers in the field of consensus control since the communication connection among multiple agents can randomly change with time and space. Following this pattern, this paper models the communication topology with the Markovian randomly switching graphs, since the Markovian chain process is usually used to model the network with Rayleigh fading channel. In this stochastic framework, this paper focuses on the consensus control and performance improvement problems of grouped agents with linear or linearized nominal dynamics. To solve this problem, a class of state-feedback controllers is proposed under the assumption that all the state measurements are available. These controllers are intrinsically distributed since they solely require the relative information between neighboring agents. Moreover, the notion of H
_∞
(H
₂
) stochastic consensus region integrated with transient performance is defined to measure the robustness of the proposed controllers with respect to the communication topologies. This paper theoretically shows that these controllers yield unbounded consensus region, which implies that they are well-designed. Furthermore, these controllers can improve the H
_∞
H
₂
consensus, and transient performances of agents subject to external and initial-state disturbances. At the end of this paper, numerical simulations and experiments are performed to verify the theoretical results.