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• Distributed optimization problems of consensus are examined by a frequency-domain analysis approach. • An optimized distributed protocol is proposed such that the nonuniform time-delay FDMSs with SF have better consensus performance. • The double-integral dynamics of delayed FDMSs with SF is considered. This paper addresses distributed optimization problems concerning consensus in delayed fractional-order double-integrator multi-agent systems (FDMSs). To start with, an optimized distributed protocol with state-fractional-order-derivative feedback (SF) is presented for delayed FDMSs. Then, the consensus problems are studied for the two kinds of delayed FDMSs with SF in the presence of symmetric time-delays over undirected network topology and asymmetric time-delays over directed network topology. Next, by the means of graph theory, matrix theory and frequency-domain analysis method, the sufficient conditions to guarantee consensus of delayed FDMSs with SF are derived. Compared to the traditional distributed protocol without SF, the proposed distributed optimization protocol with SF are taken into account to enable better consensus performance in delayed FDMSs with SF. Finally, numerical experiments are carried out to verify the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

• An optimization problem about the state mean of multi-agent systems with impulsive noise based on MCC derived from information theoretic learning is investigated in this paper, where the half-quadratic(HQ) strategy is used to simplify the solving process of the optimization problem. • A problem interfered by impulsive noise on the states of multi-agent systems is studied in this paper, where the adverse effect of impulsive noise on the states is eliminated by the MCC algorithm. • An event-triggered consensus problem of discrete-time multi-agent systems with random impulsive noise is addressed in this paper, where an event-triggering condition is derived for the system to achieve consensus. An event-triggered consensus problem of discrete-time multi-agent systems with impulsive noise under directed switching topology is investigated in this paper, where the control input of each agent is determined by its own state information and the state information of its neighbors that may be corrupted by impulsive noise. Firstly, to reduce the adverse effect of impulsive noise on consensus performance of the discrete-time multi-agent systems, maximum correntropy criterion (MCC) derived from information theoretic learning is introduced to calculate the communication weights among the agents, and an event-triggered strategy is adopted to drive the state variables of each agent to eventually converge to a same value. Secondly, the condition to guarantee consensus of the discrete-time multi-agent systems is derived by graph theory and Lyapunov stability theorem. Finally, the effectiveness of the theory is verified by several numerical simulations. [ABSTRACT FROM AUTHOR]