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In this paper, the observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems with potentially different state dimensions and different dynamics are investigated. Considering the agents' states may be not available in practice, the distributed state observer is designed for each agent. Then corresponding distributed control protocols based a proposed virtual exosystem are proposed to convert the output consensus problem into the stabilisation problem. By employing matrix theory, algebraic graph theory and the stability theory of fractional system, the state consensus of the virtual exosystem and the output consensus of heterogenous fractional nonlinear MAS is achieved. Moreover, the sufficient conditions are also obtained. Simulation examples are presented to verify the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of mean square consensus for nonlinear multi-agent systems with state-dependent noise perturbations. A distributed event-triggered mechanism which can be used to reduce the number of controller updates and communication load is developed to apply in stochastic dynamical systems. By combining the tools of graph theory and stochastic analysis, the sufficient conditions are given to ensure that mean square consensus in the multi-agent systems can be achieved exponentially. The convergence rate is also analytically derived. Moreover, the feasibility of the proposed distributed event-triggered strategy is further verified by exclusion of Zeno behaviour. Finally, some numerical examples are given to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the quasi-containment control problem of fractional-order multi-agent systems (FOMASs). First, to reduce the frequency of communications, a novel observer-based event-triggered control mechanism which only relies on the information at the trigger-time is proposed. And then, by applying the theory of algebraic graph, matrix and fractional-order calculus, some sufficient consensus conditions based on the linear matrix inequality are established for achieving the consensus of FOMASs. In addition, the strict positive lower bound on the inter-event interval is obtained, which implies that the system is free from the Zeno behaviour. Finally, several simulation examples are presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the authors consider the consensus tracking problem for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state. The dynamics of each agent consists of nonlinear inherent dynamics. In order to reach consensus tracking, a class of nonsmooth control protocols is proposed which only depends on the agent's own information and its neighbours’ information. With the aid of algebraic graph theory, matrix theory, and Lyapunov theory, some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived. Finally, the numerical simulations are given to illustrate the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

The distributed formation control of fractional-order multi-agent systems is mainly studied under directed interaction topology in this paper. First, the control algorithm with absolute damping and communication delay is proposed to achieve the formation control. Then, some sufficient conditions are derived by using the matrix theory, graph theory and the frequency-domain analysis method. Finally, based on the numerical method of predictor–corrector, several simulations are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM PUBLISHER]

In this paper, the distributed formation control problem for multiple nonholonomic mobile robots using consensus-based approach is considered. A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Distributed control laws are developed for achieving the formation control objectives: a group of nonholonomic mobile robots at least exponentially converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. Rigorous proofs are provided by using graph, matrix , and Lyapunov theories. Simulations are also given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, the multistage homotopy-perturbation method (HPM) is applied to realize the synchronization between the Lorenz system and the Chen system using active control. The multistage HPM is only a simple modification of the standard HPM, in which it is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions. The simulation results reveal that the multistage method is an effective tool to give the approximate analytical solutions for chaotic systems. [ABSTRACT FROM AUTHOR]