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This paper investigates the distributed control of multi-agent systems (MASs) with objective optimization on directed detail-balanced networks, in which the global optimization function is expressed as a convex combination of local objectives of agents. First, a directed and detail-balanced network depending on the weights of an optimization function is constructed, and a distributed consensus protocol with gradients of local objectives is proposed over the designed network. Using Lyapunov stability theory and a projection technique, we prove that the proposed protocol not only makes all agents achieve consensus in a fixed-time interval but can also solve the global optimization problem asymptotically. Moreover, the optimization problem with box constraints is studied, and a δ -exact penalty method is employed to eliminate the constraints. Similarly, a distributed fixed-time consensus protocol with gradient measurement is developed, and we prove that the optimal solution can be reached asymptotically. Finally, two examples are presented to show the efficacy of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we are interested in the problem of modeling, analysis and control of rumor spreading on online social networks. As the diversity of languages and the difference of user nodes in the network, a heterogeneous rumor spreading model with two language spreaders is proposed, and the impulsive isolation control strategy is considered. Firstly, the model with periodic impulsive isolation control and time-delay recovery rate is discussed. Based on the stability theory of impulsive differential equations, some conditions regarding the impulsive period and control gains are given for the rumor asymptotically disappearance and persistent existence. Secondly, a new type of event-triggered impulsive isolation control method is developed to address the tradeoff between restraining rumor and minimizing the cost of control, and some conditions are given to make the rumor disappear asymptotically. Furthermore, an improved event-triggered mechanism is established based on the fixed-time stability theory, which provides the conditions for the rumor to disappear within a fixed-time. Finally, some numerical simulations and an actual example are given to verify the rationality of the model and the effectiveness of the control methods. • A new rumor propagation model with impulsive isolation control is proposed. • Periodic and event-triggered aperiodic impulsive control strategies are proposed. • The fixed-time control of rumor propagation is studied in the first time. [ABSTRACT FROM AUTHOR]

Online social networks (OSNs), as multilingual communication platforms, provide great convenience for rumor spreading. However, a great deal of negative impacts on individuals, society and economy will be caused during the spread of rumor. In order to explore the rules of rumor propagation on online social networks and formulate the corresponding control strategies, in this paper, we propose new 2I2SR rumor propagation models with and without time-delay based on multilingual environment. Firstly, we calculate the basic reproduction number which completely determines the local and global stability of the rumor free equilibrium. Secondly, our theoretical analysis reveals the existence and stability of the rumor equilibria, and some critical conditions are obtained for the existence of Hopf bifurcation by selecting critical parameters and delay as bifurcation parameters. Furthermore, by using Pontryagin's Maximum principle, a real-time optimization method that minimizes the cost of restraining rumor is proposed to eliminate the rumor within an expected time period. Finally, some numerical simulations and a practical application are given to prove the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed control problem of single-input high-order multi-agent systems (MASs). Firstly, a nonlinear observation system is proposed to track the target system in a finite-time, and a distributed event-triggered protocol is designed to reduce the frequency of data transmission. Moreover, we popularize the distributed event-triggered algorithm to general directed networks. Applying the tree-type error method and implicit Lyapunov functions, some criteria are derived to ensure the finite-time observation and asymptotical consensus. Furthermore, based on single-output state, a fixed-time nonlinear observer is introduced, and the asymptotical consensus is also considered utilizing the distributed event-triggered protocol. Finally, the effectiveness of the control strategies is demonstrated via some numerical simulations. [ABSTRACT FROM AUTHOR]