Adaptive leader-following consensus in multi-agent systems with second-order nonlinear dynamics and directed switching topologies

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

This paper studies the observer-based leader-following consensus of a linear multiagent system on switching networks, in which the input of each agent is subject to saturation. Based on a low-gain output feedback method, distributed consensus protocols are developed. Under the assumptions that the networks are connected or jointly connected and that each agent is asymptotically null controllable with bounded controls and detectable, semiglobal observer-based leader-following consensus of the multiagent system can be reached on switching networks. A numerical example is presented to illustrate the theoretical results.

In this paper, a time-varying leader-following consensus of multi-agent systems under fixed, connected and undirected communication topology is presented. In the proposed method, the dynamics of each agent including the followers and their corresponding leader is a linear nth order system. Moreover, the communication topology between the leader and its neighbours depends upon bounded and time-varying functions, assumed to remain connected as time passes. To tackle this problem, a set of time-varying distributed control laws for each follower agent is designed, based on algebraic graph theory, algebraic Riccati equation and Lyapunov direct method. Simulation results indicate the effectiveness of the proposed method and display convergence to consensus is achieved in a finite time via time-varying distributed control laws.

This paper investigates the problem of leader-following consensus of a linear multi-agent system on a switching network. The input of each agent is subject to saturation. Low gain feedback based distributed consensus protocols are developed. It is established that, under the assumptions that each agent is asymptotically null controllable with bounded controls and that the network is connected or jointly connected, semi-global leader-following consensus of the multi-agent system can be achieved. Numerical examples are presented to illustrate this result.

This paper focuses on addressing consensus and flocking issues in second-order nonlinear multi-agent systems (MASs) under the false data injection attacks. Novel adaptive control protocols are proposed to effectively mitigate the impact of these attacks by updating adaptive parameters. Based on algebraic graph theory, matrix theory and the Lyapunov approach, various sufficient conditions are established, which show the fixed-time consensus and finite-time flocking can be achieved for the MASs. Moreover, some upper bounds for the settling time are derived in terms of the parameters of the model. Finally, three simulation examples are presented to validate the efficacy of our proposed theoretical results.

With the development of swarm intelligence in last decades, consensus problem of multi-agent systems has been attracting much attention. To reveal the inherent mechanism of leader-following consensus in multi-agent systems with stochastic dynamics, PI control protocols are designed in this paper. Owing to the stochastic analysis techniques, algebraic graph theory, and constructing appropriate Lyapunov function, it is proved that the leader-following consensus of nonlinear stochastic dynamical multi-agent systems can be reached in mean square. Sufficient condition are deduced to select the PI control protocol parameters. Finally, the theoretical results are demonstrated through a simulation example.

This paper proposes two consensus algorithms for second-order nonlinear multi-agent dynamics. The objective of the algorithms is to guarantee two states of each agent reach consensus. Consensus is achieved asymptotically based on two "virtual states" in each agent. Both of the consensus algorithms use backstepping control to deal with the nonlinear section in each agent. By the first algorithm, the consensus is achieved for agent's models without unknown parameters under switching topologies. Adopting the adaptive theory, the second algorithm solves the consensus problem for second-order nonlinear multi-agent systems with unknown parameters under a fixed topology. Simulation results show the effectiveness of the proposed algorithms.

Lag consensus means that the corresponding state vectors of the followers are behind the leader with a lag time. In this paper, Lyapunov functional and matrix theory are applied to analyze pinning-controlled lag consensus of second-order nonlinear multiagent systems. The focus is twofold: 1) to find out which agents should be pinned and 2) to determine what the coupling strength should be, so that the multiagent systems can reach lag consensus. Moreover, the practical problem in a noisy environment is considered. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed pinning control protocol.

In this paper consensus in second-order multi-agent systems with a non-periodic sampled-data exchange among agents is investigated. The sampling is random with bounded inter-sampling intervals. It is assumed that each agent has exact knowledge of its own state at all times. The considered local interaction rule is PD-type. The characterization of the convergence properties exploits a Lyapunov-Krasovskii functional method, sufficient conditions for stability of the consensus protocol to a time-invariant value are derived. Numerical simulations are presented to corroborate the theoretical results.

Integral sliding-mode fixed-time consensus tracking for second-order non-linear and time delay multi-agent systems

This letter studies the distributed adaptive consensus problem for multi-agent systems (MASs) subject to nonlinearly parameterized uncertainties. In the existing research, an adaptive consensus scheme was developed for the same scenario but under the assumption that the uncertainties must be linearly parameterized in their unknown parameters. In this letter, the assumption is removed by using a novel distributed adaptive update law, which makes the scheme applicable for more general nonlinear MASs. This letter contains a general design paradigm using the certainty equivalence principle and specific implementation of it on nonlinear second-order MASs. The results are supported by rigorous mathematical analysis and numerical simulation.

This note addresses the adaptive consensus problem of first-order and second-order linearly parameterized multi-agent systems with unknown identical control directions. First, we propose a new Nussbaum-type function based on which a key lemma is established. The lemma plays an important role in analyzing the consensus of the closed-loop multi-agent systems. Second, the Nussbaum-type function is used to design adaptive control laws for first-order and second-order linearly parameterized multi-agent systems so that each agent seeks for the unknown control direction adaptively and cooperatively. Then, under the assumption that the interconnection topology is undirected and connected, it is proved that the first-order and second-order multi-agent systems can achieve consensus by choosing proper design parameters. Two simulation examples are given to illustrate the effectiveness of the proposed control laws.

Scaled consensus of second-order nonlinear multi-agent systems with distributed adaptive control via non-reduced order method

Based on PD and PI control methods, the lag output consensus problem for second-order nonlinear multiagent systems (MASs) without and with external disturbances is addressed, which generalizes the existing lag consensus results for MASs. Firstly, a lag output consensus condition is derived for the MAS by designing a proper PD control scheme. Furthermore, a PI control strategy is developed to ensure that the MAS realizes the lag output consensus. In addition, two lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> output consensus criteria are also established on the basis of PD and PI control schemes for the MAS with external disturbances. Lastly, two examples are utilized to verify the correctness and effectiveness of the devised control schemes. Note to Practitioners—Recently, virtual leader-based approach has been widely utilized to address the output consensus control problem for various MASs. Practically, each agent receiving its own output information may be later than the virtual leader. Therefore, it is more reasonable and meaningful to discuss the lag output consensus for MASs. Furthermore, considering that PID control is very simple and easy to implement, some PD and PI control strategies are developed to tackle the lag output consensus for MASs. In addition, since external disturbances are ubiquitous and may destroy the lag output consensus, the lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathcal {H}}_{\infty } $ </tex-math></inline-formula> output consensus for MASs is also investigated. Multiple single-link robot systems experiments verify that the approaches given in this paper are feasible and valid.

This paper studies fixed-time consensus of second-order leader-following multi-agent systems with inherent nonlinear dynamics. Firstly, a new fixed-time consensus protocol is designed to solve the tracking problem of the second-order nonlinear systems. By using Lyapunov theory and graph theory, we choose a different Lyapunov function candidate to verify the theoretical results. Then we consider the second-order multi-agent systems with multiple leaders and propose a new protocol to solve the fixed-time containment control problem. Finally, two numerical examples are proposed to demonstrate the effectiveness of the proposed fixed-time protocols.