Matrix-Scaled Consensus of Uncertain Networked Systems

This paper studies the distributed matrix-scaled consensus, which can be treated as a kind of generalized cooperative control problem and has broad applications in the field of social network and engineering. Distributed protocols are expected to achieve cluster consensus with respect to the matrix-based weight and deal with the unknown disturbances present to the system dynamics. A static distributed protocol is first presented, including a linear term and a nonlinear term based on the sliding-mode control technique, under which the matrix-scaled consensus is realized and the disturbances are resisted. Then, a distributed adaptive algorithm is designed by using the adaptive method to introduce time-varying gains, obeying differential equations. It is to be pointed out that the static protocol is more concise if the parameter condition is satisfied, and the adaptive protocol is completely distributed and relies on no global information when designing or using the algorithm. Simulation examples are provided to further verify the designed algorithms.