Stochastic scaled consensus for high‐order multi‐agent systems in a noisy environment

Abstract Investigation is conducted for the mean square scaled consensus issue for high‐order stochastic multi‐agent systems (SMASs) in the presence of noise. Scaled consensus indicates that each agent asymptotically converges to a specified constant in a certain proportion rather than converge to a common value. To cope with the Laplacian matrix asymmetry problem caused by directed graphs, the concept of generalized algebraic connectivity is introduced to characterize the capability of directed networks for the consensus issue of SMASs. A distributed stochastic approximation dynamic output feedback controller is proposed to obtain the convergence for high‐order SMASs by the stochastic Lyapunov method and Itô's formula. In addition, the convergence rate for high‐order SMASs with communication noise is addressed, in which the convergence rate for our underlying system has a closed relationship with stochastic approximation time‐varying gain. Lastly, a simulation example is applied to demonstrate the validity of the results.