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Distributed consensus tracking for the fractional-order multi-agent systems is mainly studied in this paper. Firstly, the simple Lyapunov candidate function is discussed to judge the validity of the proposed controller. Secondly, according to the sliding mode control method, a controller is designed to achieve the consensus tracking problem when the followers are described by the fractional-order linear dynamics. Thirdly, the case when the dynamics of followers own the intrinsic nonlinear function is discussed, it proves that the designed sliding mode controller is still valid for this case under the certain conditions. For the above two parts, the systems stabilities are judged based on the result of the first part. Finally, several simulations are presented to verify the obtained results. [ABSTRACT FROM AUTHOR]

• The finite-time and fixed-time bipartite consensus of MASs over signed graph while considering both leaderless and leader-following MASs are investigated. • In contrast to the existing methods to address FNTBC and FXTBC, the impulsive control was employed, which has a better performance in convergence speed and less state information transmission. • Some sufficient criteria and the settling time which are based on the proposed impulsive control protocols are derived. This paper studies the finite-/fixed-time bipartite consensus (FNTBC and FXTBC) of multi-agent systems (MASs) over signed graph via discontinuous impulsive control while considering both leaderless and leader-following MASs. In contrast to the existing methods of FNTBC and FXTBC, the impulsive control has a better performance in convergence speed and less state information transmission, which is more practical and flexible in real applications. To realize FNTBC and FXTBC for leaderless and leader-following MASs, a class of distributed impulsive control protocols is proposed. Then by utilizing impulsive control theory and finite-/fixed-time stability theory, some sufficient criteria and the settling time which are based on the proposed impulsive control protocols for FNTBC and FXTBC for leaderless and leader-following MASs are derived. It has been shown that the settling time for FNTBC depends on initial conditions of systems, while this limitation is removed for FXTBC. Finally, the proposed impulsive protocols are validated by some simulations, separately. [ABSTRACT FROM AUTHOR]

This paper investigates group consensus of a class of heterogeneous multi-agent systems with input saturation via pinning scheme, in where the heterogeneous multi-agent system is composed of first-order agents and second-order agents. Firstly, based on the fact that the control input of partial first-order integrator agents could be bounded due to the limitation of actuators, a class of control protocols including partial first-order integrator agents with input saturation is proposed to solve the group consensus problem of heterogeneous multi-agent systems. Secondly, to guarantee the states of agents in the same group can converge to one specified consensus state, the group consensus problem of heterogeneous multi-agent systems with some pinned agents who can be first-order or second-order agents is discussed. Then a class of new control protocols with pinning scheme is proposed. By using LaSalle Invariance Principle, matrix theory, algebraic graph theory and Lyapunov stability theory, the rigorous proofs are given and the corresponding sufficient group conditions are also obtained. Finally, simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics group consensus problem of heterogenous multi-agent systems with time delays, in which agents’ dynamics are modeled by single integrators and double integrators. To achieve group consensus, a class of dynamics group consensus protocols is proposed for heterogenous multi-agent systems with input time delays, which can also be used to solve group consensus for heterogenous multi-agent systems without input time delays. By using frequency-domain analysis method and matrix theory, some sufficient group consensus conditions, which are dependent on the input delays and the control parameters, are obtained for heterogenous multi-agent systems under directed and undirected communication topologies with and without input time delays, respectively. Simulation results are also provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: Hybrid projective synchronization of fractional order chaotic systems with time-delay is investigated. It is shown that the slave system can be synchronized with the driver up to a scaling matrix. According to the stability theorem of linear fractional order systems with multiple time-delays, a nonlinear controller is proposed for the synchronization. Finally, two different structural time-delayed fractional order chaotic systems are applied to realize hybrid projective synchronization. The corresponding numerical results show the effectiveness and robustness of the controller. [Copyright &y& Elsevier]

This paper addresses the fixed-time formation tracking problem of multi-robot systems with nonholonomic constraints. A new type of distributed nonlinear controller for each robot is designed. Some corresponding sufficient conditions are derived by using algebraic graph theory, matrix analysis and fixed-time stability theory. In addition, an upper bound of the settling time for the multi-robot systems is also explicitly given. It is shown that the obtained upper bound of settling time is regardless of initial errors of systems, which implies that it can facilitate the pre-design of the convergence time off-line. Numerical example is provided to illustrate the effectiveness of the present theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed formation tracking problem of multi-robot systems with nonholonomic constraint via event-triggered approach. A variable transformation is firstly given to convert the formation tracking problem into the consensus-like issue. Then a novel type of distributed event-triggered control strategy is proposed under fixed topology and switching topology, which can guarantee multi-robot systems to produce desired geometric configuration from arbitrary initial positions and orientations for each robot, while the centroid of formation can follow one dynamic reference trajectory. Moreover, the novel event-triggering conditions under fixed topology and switching topology, which only need intermittent interaction between neighboring robots, are designed to assist the execution of distributed controllers. Based on the designed event-triggering conditions, the robot systems can effectively reduce the communication cost, energy consumption and mechanical wear, especially when the quantity of robots is huge. Finally, the effectiveness of theoretical results is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive distributed formation control problem for multiple nonholonomic wheeled mobile robots. First, the formation control problem is converted into a state consensus problem by the aid of a variable transformation. Then, distributed kinematic controllers and adaptive dynamic controllers are developed for each robot such that a group of nonholonomic mobile robots asymptotically converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. The specified reference trajectory is assumed to be the trajectory of a virtual leader whose information is available to only a subset of the followers. Also the followers are assumed to have only local interaction. Some sufficient conditions are derived for accomplishing the asymptotically stability of the systems based on algebraic graph theory, matrix theory, and Lyapunov control approach. Finally, simulation examples illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. [Copyright &y& Elsevier]

• The containment control of fractional order multi-agent systems with nonlinearity is considered. • A control protocol with time delay for fractional order multi-agent systems is designed. • A pull-based event-triggered control law combined time delay is designed. • Mittag-Leffler function based method is adopted instead of Lyapunov method. • Zeno behavior is precluded by the strict proof. The containment control for fractional order multi-agent systems with nonlinearity and time delay is investigated in this article. Firstly, a distributed control protocol with fixed time delay is proposed for the purpose of achieving containment control for nonlinear fractional order multi-agent systems. Secondly, by using the pull-based event-triggered mechanism, a distributed event-based control law with time delay is further given to accomplish containment control for fractional order multi-agent systems with nonlinearity. In this way, the controller of each agent is merely updated at its own trigger moments. Hence, it can decrease network correspondence congestion and lower computational cost. Thanks to the stability theory of fractional order calculus, matrix theory, and properties of Mittag-Leffler function, the feasibility of the designed control protocols is confirmed. Furthermore, the Zeno behavior is precluded by the strict proof. Ultimately, two simulation examples are used to illustrate the availability of above theoretical analysis respectively. [ABSTRACT FROM AUTHOR]

Abstract The problem of disturbance rejection/attenuation for constant-input delayed linear multi-agent systems (MASs) with the directed communication topology is tackled in this paper, where a classic model reduction technique is introduced to transform the delayed MAS into the delay-free one. First, when the leader has no control input, a novel adaptive predictive extended state observer (ESO) using only relative state information of neighboring agents is designed to achieve disturbance-rejected consensus tracking. The stabilization analysis is presented via the Lyapunov function and sufficient conditions are derived in terms of linear matrix inequalities. Then the result is extended to disturbance-attenuated case where the leader has bounded control input which is only known by a portion of followers. Finally, two numerical examples are presented to illustrate the effectiveness of proposed strategies. The main contribution focuses on the design of adaptive predictive ESO protocols with the fully distributed property. [ABSTRACT FROM AUTHOR]