Second-order Nonlinear Multi-agent Systems Research Articles

Consensus of a class of second-order nonlinear heterogeneous multi-agent systems with uncertainty and communication delay

Summary In this paper, a consensus problem is studied for a group of second-order nonlinear heterogeneous agents with non-uniform time delay in communication links and uncertainty in agent dynamics. We design a class of novel decentralized control protocols for the consensus problem whose solvability is converted into stability analysis of an associated closed-loop system with uncertainty and time delay. Using an explicitly constructed Lyapunov functional, the stability conditions or the solvability conditions of the consensus problem are given in terms of a set of linear matrix inequalities apart from a small number of scalar parameters that appear nonlinearly. Furthermore, the linear matrix inequalities are theoretically verified to be solvable when the communication delay is sufficiently small. The effectiveness of the proposed control protocol is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Leader-following consensus for a class of second-order nonlinear multi-agent systems

This paper deals with the leader-following consensus problem for a class of multi-agent systems with nonlinear dynamics and directed communication topology. The control input of the leader agent is assumed to be unknown to all follower agents. A distributed adaptive nonlinear control law is constructed using the relative state information between neighboring agents, which achieves leader-following consensus for any directed communication graph that contains a spanning tree with the root node being the leader agent. Compared with previous results, the nonlinear functions are not required to satisfy the globally Lipschitz or Lipschitz-like condition and the adaptive consensus protocol is in a distributed fashion. A numerical example is given to verify our proposed protocol.

Cooperative Global Output Regulation of Second-Order Nonlinear Multi-Agent Systems With Unknown Control Direction

This technical note addresses the cooperative global output regulation problem for second-order nonlinear multi-agent systems without a priori knowledge of the control direction. We will propose both the graph-dependent and graph-independent distributed controllers based on the combination of the internal model, the Nussbaum-type dynamic gain, and the adaptive control technique. Comparing with some existing results, our novel design can handle the multi-agent system with not only the arbitrary and non-identical unknown control direction but also the uncertain parameter that belongs to any unknown and non-compact set.

Neural‐network‐based adaptive leader‐following consensus control for second‐order non‐linear multi‐agent systems

In this study, a novel adaptive neural network (NN)-based leader-following consensus approach is proposed for a class of non-linear second-order multi-agent systems. For the existing NN consensus approaches, to obtain the desired approximation accuracy, the NN-based adaptive consensus algorithms require the number of NN nodes to must be large enough, and thus the online computation burden often are very heavy. However, the proposed adaptive consensus scheme can greatly reduce the online computation burden, because the adaptive adjusting parameters are designed in scalar form, which is the norm of the estimation of the optimal NN weight matrix. According to Lyapunov stability theory, the proposed approach can guarantee the leader-following consensus behaviour of non-linear second-order multi-agent systems to be obtained. Finally, a numerical simulation and a multi-manipulator simulation are carried out to further demonstrate the effectiveness of the proposed consensus approach.

Distributed finite-time containment control for second-order nonlinear multi-agent systems

This paper considers the finite-time containment control problem for a class of second-order nonlinear multi-agent systems with external disturbances under the directed topology graph. The considered nonlinear systems are composed of multiple dynamic leaders, and they have only a subset of the followers with their accessing to the leaders. Firstly, by using the one-hop neighbors’ information, a second-order finite-time distributed observer estimator protocol is constructed to achieve accurate estimation of the weighted average of the velocities and positions of the leaders. Furthermore, it is proved that the proposed estimator protocol can guarantee accurate estimation of the weighted average of the velocities and positions of the leaders in the finite-time. Then, we design a new continuous nonlinear control protocol by means of the nonsingular terminal sliding mode. It is shown that by using proposed control protocol, the states of the followers can converge to the convex hull spanned by those of the leaders in the finite-time. In addition, the finite convergence time can be also explicitly estimated. Finally, the effectiveness of the obtained theoretical results is illustrated by the numerical simulation.

Lag consensus of the second-order leader-following multi-agent systems with nonlinear dynamics

Lag consensus is a phenomenon where followers track the trajectory of the leader with a time delay. By using lag consensus, a protocol is designed for agents to behind the leader at different times, so as to avoid congestion. In this paper, aiming to the lag consensus of second-order nonlinear multi-agent systems, a control protocol for each follower based on local information of neighboring agents is proposed, and an adaptive feedback control protocol is also given. Moreover, the multi-agent systems with noisy environment are considered. The results suggest that our protocol is robust to the noise. Finally, simulation examples are given to illustrate our theoretical analysis.

Synchronization of nonlinear systems with communication delays and intermittent information exchange

This paper studies the synchronization problem of second-order nonlinear multi-agent systems with intermittent communication in the presence of irregular communication delays and possible information losses. The control objective is to steer all agents’ positions to a common position with a prescribed desired velocity available only to some leaders. Based on the small-gain framework, we propose a synchronization scheme relying on an intermittent information exchange protocol in the presence of time delays and possible packet dropouts. We show that our control objectives are achieved with a simple selection of the control gains provided that the directed graph, describing the interconnection between agents, contains a spanning tree. An example of Euler–Lagrange systems is considered to illustrate the application and effectiveness of the proposed approach.

Distributed containment control for bounded unknown second-order nonlinear multi-agent systems with dynamic leaders

This paper investigates distributed containment control problems for second-order nonlinear multi-agent systems with dynamic leaders. In the presence of bounded unknown nonlinearity, a distributed control algorithm based on High-frequency Feedback Robust Control is proposed. Under this algorithm, a sufficient condition is proposed to ensure that all the followers will converge to the dynamic convex hull formed by dynamic leaders and the containment error can be ultimately bounded for the directed graph where at least one leader has a directed path to each follower and the communication among the followers are undirected. Numerical simulations are also presented to illustrate the effectiveness of the theoretical results.

Sliding mode leader‐following consensus controllers for second‐order non‐linear multi‐agent systems

This study discusses the asymptotic consensus problem and finite-time leader-following consensus problem of second-order non-linear multi-agent systems (MASs) with directed communication topology. On the basis of the sliding mode control theory, a new distributed asymptotic consensus controller is proposed to ensure that the consensus of MAS can be reached as time goes to infinity. Another finite-time consensus control algorithm is also proposed based on terminal sliding mode control. The finite-time consensus controller can force the states of MAS to achieve the designed terminal sliding mode surface in finite time and maintain on it. The authors also can prove the consensus of MAS can be obtained in finite time on the terminal sliding mode surface if the directed topology has a directed spanning tree. Simulations are given to illustrate the effectiveness of the proposed approaches.

Consensus of second-order nonlinear multi-agent systems under state-controlled switching topology

This paper studies the consensus problem of second-order multi-agent systems under both fixed and switching directed topologies in a more general framework. Specifically, each agent incorporates an intrinsic nonlinear dynamics and the communication topology switches in a state-controlled manner. Novel distributed consensus protocols are proposed based only on relative position information and local velocity information. Through constructing appropriate Lyapunov functions, it is shown that the proposed protocols are feasible for achieving consensus, even under switching topology jointly containing a spanning tree. Moreover, some easily manageable algebraic criteria are presented to unravel the underlying mechanism for reaching consensus. In the special case of multi-agent systems with double-integrator dynamics, we further derive a necessary and sufficient condition for the consensus problem. Finally, two numerical examples are provided to validate the effectiveness of theoretical results.

Distributed Adaptive Consensus of Nonlinear Multi-agent Systems with Unknown Control Coefficients

This paper is devoted to the leader-follower consensus problem for nonlinear multi-agent systems. Remarkably, the control coefficients in the systems are unknown which makes the problem rather difficult to solve. By employing the distributed adaptive protocols, the consensus is achieved under undirected connected graph for the first-order nonlinear multi-agent systems. Furthermore, similar results for the general case are obtained for the second-order nonlinear multi-agent systems. At last, two simulation examples are given to show the effectiveness of the protocols.

Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design

This paper considers the leader-following tracking problem of second-order nonlinear multi-agent systems with a reference leader. It is assumed that all following agents can only access the relative position information with its neighbors, the position and velocity information of the leader is only accessed by a subset of the following agents, and the leader׳s bounded reference input cannot be available by any following agents. To track the active leader, a distributed discontinuous observer-based consensus protocol is proposed for each following agent, whose observer is used to estimate the agent׳s unmeasured velocity. Under connected undirected interaction topology, the proposed protocol can be used to solve the second-order nonlinear multi-agent consensus problem. While the reference input of the leader is known, the proposed protocol can solve the consensus problem under a class of directed switching interaction topologies. Furthermore, to make the designed approach in fully distributed fashion, the distributed adaptive laws are provided to design the protocol coupling parameters. Finally, a numerical example is presented to illustrate our obtained result.

Observer-based consensus for nonlinear multi-agent systems with intermittent communication

The article studies a consensus control problem for second-order nonlinear multi-agent systems with a leader where the velocity of the active leader cannot be obtained in real time. Under the common assumption that the multiple agents can communicate with their neighbors only during a sequence of discontinuous time intervals, a new neighbour-based consensus control protocol based on observers is developed for each agent. With the help of multiple Lyapunov function technology, some sufficient conditions are derived such that the follower agents can track the leader and keep pace with the leader at the same time under fixed topology. Moreover, the similar results are given under the switching topology. Finally, numerical examples are presented for illustration.

Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control

This paper considers the problem of finite-time synchronization for a class of second-order nonlinear multi-agent systems with a leader-follower architecture. By using the finite-time control technique and homogenous systems theory, a finite-time state feedback controller is first proposed. Then to address the lack of velocity measurement, a finite-time convergent observer is constructed to estimate the unknown velocity information in a finite time. Finally, an observer-based finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader's states. In addition, for some special second-order multi-agent systems, a bounded finite-time output feedback controller can also be designed.

Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

Second-order group consensus for multi-agent systems via pinning leader-following approach

This paper addresses the group consensus problem of second-order nonlinear multi-agent systems through leader-following approach and pinning control. The network topology is assumed to be directed and weakly connected. The pinning consensus protocol is designed according to the agent property, that is, the inter-act agent and the intra-act agent. Some consensus criteria are proposed to guarantee that the agents asymptotically follow the virtual leader in each group, while agents in different groups behave independently. Numerical example is also provided to demonstrate the effectiveness of the theoretical analysis.

Impulsive Formation Control Algorithms for Leader-following Second-order Nonlinear Multi-agent Systems

This paper investigates second-order nonlinear multi-agent systems with fixed and switching topologies. For the delay multi-agent system with fixed topology, an impulsive formation control strategy is proposed which only operates at instant times. Based on some impulsive time-delay differential inequalities, the sufficient conditions that ensure the nonlinear multi-agent systems converge to a desired formation are established. Furthermore, the results obtained are extended to the case when the interaction topology is switching. For the multiagent with disturbance under switching topology, the sufficient condition is obtained under the impulsive control. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.

Delay-Distribution-Dependent Consensus for Second-Order Leader-Follower Nonlinear Multiagent Systems via Pinning Control

This paper investigates the consensus problem for second-order leader-follower nonlinear multiagent systems with general network topologies. A pinning control algorithm is proposed, where it includes time-varying delay information. By using the information of delay-partition and delay-distribution and constructing an appropriate Lyapunov-Krasovskii functional, the consensus criteria are derived to achieve leader-follower consensus for multiagent systems, which are in the form of linear inequalities that can be solved by employing the semidefinite programme method. Moreover, this paper addresses what kind of agents and how many agents should be pinned. Two numerical examples are presented to further demonstrate the effectiveness of the proposed approach.

Second-order consensus with unknown dynamics via cyclic-small-gain method

This study proposes a distributed non-linear consensus protocol for second-order non-linear multi-agent systems with unknown locally Lipschitz dynamics and connected graph. The main analysis is based on a blend of graph-theoretic and non-linear-theoretic tools with the notion of input-to-state stability (ISS) playing a central role. Through the backstepping design, the closed-loop multi-agent system is transformed into a two-cascade interconnected system with proven ISS properties. Correspondingly, the recently developed cyclic-small-gain theorem is then employed to guarantee the asymptotic stability of the closed-loop multi-agent system, which implies consensus.

Leader-following formation control of multi-agent systems under fixed and switching topologies

In this article, two kinds of leader-following formation control problems for second-order nonlinear multi-agent systems are investigated, that is, the cases with fixed topology and with switching topology. For the former, by constructing an appropriate Lyapunov functional and utilising linear matrix inequality (LMI) method, we propose a formation control algorithm which makes the nonlinear multi-agent systems converge to a desired formation. In addition, a formation control algorithm is also developed for coupled double-integrators with a constant reference velocity. Then we extend these results to the case when the interaction topology is switching. Numerical simulations are presented finally to demonstrate the effectiveness of the proposed results.