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This work is dedicated to the leaderless/leader-following stochastic scaled consensus issue of second-order stochastic multi-agent systems (SMASs) in a noisy environment. Scaled consensus represents that the ratios among agents asymptotically tend to designated constants rather than the common convergence value. To lessen the influence of communication noise, some stochastic approximation protocols with time-varying gain are designed for our underlying system, where the time-varying gain remove the restriction of nonnegative value. Compared with the existing consensus results with communication noise, the major challenge is that the introduction of time-varying gain results in the inapplicability of Lyapunov-based technique. To cope with it, a state decomposition method is utilized, and a series of sufficient necessary conditions are set up for interacting agents with constant velocity and zero velocity if the topology includes a spanning tree. Furthermore, it is conducted that the consensus and bipartite consensus can be seen as two special cases of our work. Finally, the validity of our results is demonstrated by a simulation example. • The derived theoretical results are capable for leaderless and leader-following scaled consensus of second-order SMASs, despite the presence of communication noise. • A time-varying gain is utilized to reduce the negative impact of communication noise, and the time-varying gain removes the restriction of positive time-varying gain. • Moreover, we consider the scaled consensus models without or with a negative velocity feedback. We find that the negative velocity feedback does not affect the convergence of the velocity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the distributed control problem for multi-agent systems (MASs) subject to multiplicative and additive noises over switching networks, where both cooperative and antagonistic interactions coexist. The communication topology is governed by a continuous-time Markovian chain. A stochastic approximation technique is utilized to handle stochastic bipartite consensus with communication noises. The major challenge, due to the fact that the intensity of the multiplicative noise is nonlinearly coupled with the distance between agents, is that the coexistence of antagonistic information and multiplicative noise makes the multiplicative noise term impossible to be converted into an error form. This leads to the inapplicability of the Lyapunov-based method. To cope with this, we first show the boundedness of agents' states where the second moment approach is employed. Based on it, the mean square and almost surely bipartite consensus are achieved under some mild requirements. The efficiency of the proposed method is supported by an example. [ABSTRACT FROM AUTHOR]

In this paper, the bipartite consensus problem for second-order multi-agent systems with no leader, one leader and multiple leaders are investigated, where the information exchange is disturbed by measurement noise and antagonistic information. In order to attenuate the effect of communication noise, a time-varying gain c (t) is utilized and the stochastic approximation bipartite control protocol is proposed. It is given that the underlying protocol can solve the bipartite consensus problem for MASs with no leader/one leader/multiple leaders if the communication topology is strongly connected/has a spanning tree/has a spanning forest and the c (t) satisfies some mild condition. Meanwhile, for system with these three cases, a series of sufficient and necessary conditions are given. Especially, for the case with no leader, we obtain that the final state of agent is related with the initial position and initial velocity of each agent. For the case with one leader, we can get that the followers in one group can follow up the state of one leader, and the followers in another group tend to the opposite value. Additionally, for the case with multiple leaders, the containment control can be achieved where followers' states in one group can converge to the quai-convex hull of leaders' state and the ones in another group converge to the opposite convex hull. Finally, some numerical examples are given to support our new results. [ABSTRACT FROM AUTHOR]