General Linear Node Dynamics Research Articles

Robust node‐to‐node consensus of linear multiagent systems with directed switching topologies subject to uncertain pinning communications

SummaryThis paper is focused on the node‐to‐node consensus problem of multiagent systems consisting of general linear node dynamics under directed switching topologies. Specifically, it is assumed that the multiagent systems under consideration have 2 layers, ie, leader layer and follower layer. When uncertainties on the pinning links between the 2 layers exist, the coordination goal is to present some robust control laws, which are distributed such that the states of each follower asymptotically converge to those of its corresponding leader. By using tools from M‐matrix theory and multiple Lyapunov methods, some sufficient criteria are derived to achieve this goal. Finally, 2 simulation examples are performed to validate the effectiveness of the theoretical results.

Coordination tracking of multi‐agent dynamical systems with general linear node dynamics

SummaryDistributed coordinated tracking problems are investigated in this paper for a class of multi‐agent dynamical systems with general linear node dynamics under a directed fixing interaction topology. First, a kind of class of distributed information communication protocols based on only the relative output measurements of neighboring agents is proposed and employed to realize containment tracking in multi‐leader multi‐agent linear systems. With the assumptions that the intrinsic linear dynamics of each agent are stabilizable and detectable, and each follower can be directly or indirectly affected by at least one leader, it is proven that containment tracking in the closed‐loop multi‐leader multi‐agent systems will be guaranteed if the coupling strength between neighboring agents and the gain matrices of the information communication protocols are suitably chosen. The decay rate for containment tracking errors of the considered multi‐leader multi‐agent system is also discussed. Then, consensus tracking and formation control problems of single‐leader multi‐agent systems with general linear node dynamics are respectively addressed. At last, node‐to‐node consensus tracking for multi‐agent systems with multiple coupling leaders is discussed. Simulation examples and experiment results are performed to validate the obtained results. Copyright © 2017 John Wiley & Sons, Ltd.

Consensus rate regulation for general linear multi-agent systems under directed topology

Recently, optimization in distributed multi-agent coordination has been studied concerning convergence speed. The optimal convergence speed of consensus for multi-agent systems consisting of general linear node dynamics is still an open problem. This paper aims to design optimal distributed consensus protocols for general identical linear continuous time cooperative systems which not only minimize some local quadric performances, but also regulate the consensus rate (including convergence rate and damping rate) for the multi-agent systems. The graph topology is assumed to be fixed and directed. The inverse optimal design method is utilized and the resulting optimal distributed protocols place part of close-loop poles of the global disagreement systems at specified locations asymptotically, while the remains far from the imaginary axis enough. It turns out that for the identical linear continuous time multi-agent systems, the convergence speed has no upper bound. The main advantages of the developed method over the LQR design method are that the resulting multi-agent systems can achieve specified consensus rate asymptotically and the resulting protocols have the whole right half complex plane as its asymptotical consensus region. Numerical examples are given to illustrate the effectiveness of the proposed design procedures.

Distributed robust consensus of linear multi‐agent systems with switching topologies

This paper studies the consensus problem of multi-agent systems consisting of general linear node dynamics with external disturbances in transmission channels under fixed and switching communication topologies. A distributed observer-type robust consensus protocol based on relative output measurements is proposed. A model transformation approach is introduced to address the robust consensus of multi-agent systems. Some conditions for robust consensus are given in terms of linear matrix inequalities for fixed and jointly connected communication topologies. A multi-step robust consensus protocol design procedure is further presented. Finally, the effectiveness of the theoretical results is demonstrated through numerical simulations.

Distributed consensus protocol design for general linear multi‐agent systems: a consensus region approach

This study presents a consensus region approach to designing distributed consensus protocols for multi-agent systems with general continuous-time linear node dynamics. The consensus region approach has a favourable decoupling feature, which decouples the design of the feedback gain matrices of the consensus protocols from the communication graph. Multi-step algorithms are presented to construct the fixed-gain consensus protocols, which requires the smallest non-zero eigenvalue of the Laplacian matrix. To remove this limitation, distributed adaptive protocols with time-varying coupling weights are designed for the cases with undirected and directed graphs, which can be implemented in a fully distributed fashion. The robustness issue of the adaptive protocols in the presence of external disturbances is also discussed. For the case where there exists a leader of bounded unknown control input, distributed discontinuous and continuous controllers are designed to solve the distributed tracking problem.

Distributed robust control of uncertain linear multi‐agent systems

SummaryIn this paper, the distributed H ∞ robust control problem synthesized with transient performance is investigated for a group of autonomous agents governed by uncertain general linear node dynamics. Based on the relative information between neighboring agents and some information of other agents, distributed state‐feedback and observer‐type output‐feedback control protocols are designed and analyzed, respectively. By using tools from robust control theory, conditions for the existence of controllers for solving such a problem are established. It is shown that the problem of distributed H ∞ robust control synthesized with transient performance can be converted to the H ∞ control problem synthesized with transient performance for decoupled linear systems of the same low dimensions. Finally, simulation examples are provided to illustrate the effectiveness of the design. Copyright © 2014 John Wiley & Sons, Ltd.

Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications

SUMMARY Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi-agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi-agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low-dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi-step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi-agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

A New Observer‐Type Consensus Protocol for Linear Multi‐Agent Dynamical Systems

AbstractThe consensus problem is investigated in this paper for a class of multi‐agent systems with general linear node dynamics and directed communication topologies. A new distributed observer‐type consensus protocol is designed based only on the relative output measurements of neighboring agents. Compared with existing observer‐type protocols, the one presented here does not require information about the relative states of the observers. Tools from small gain theory and matrix analysis, some sufficient conditions are obtained for achieving consensus in such multi‐agent systems where the underlying network topology contains a directed spanning tree. Finally, some numerical examples including an application in low‐Earth‐orbit satellite formation flying are provided to illustrate the theoretical results.

Distributed H ∞ consensus of multi-agent systems: a performance region-based approach

This article addresses the distributed H ∞ consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H ∞ consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H ∞ protocols is further proposed. Theoretical analysis indicates that the distributed H ∞ consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H ∞ performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Observer‐Type Consensus Protocol for a Class of Fractional‐Order Uncertain Multiagent Systems

This paper investigates the consensus problem for a class of fractional‐order uncertain multiagent systems with general linear node dynamics. Firstly, an observer‐type consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on property of the Kronecker product and stability theory of fractional‐order system, some sufficient conditions are presented for robust asymptotical stability of the observer‐based fractional‐order control systems. Thirdly, robust stabilizing controllers are derived by using linear matrix inequality approach and matrix’s singular value decomposition. Our results are in the form of linear matrix inequalities which can easily be solved by LMI toolbox in MATLAB. Finally, a numerical simulation is performed to show the effectiveness of the theoretical results.

Cooperative Tracking and Disturbance Suppression: A Classical Approach

In this paper, the cooperative tracking problem of multiagent systems with a determinate disturbance input is analyzed. The communication topology of single-input-single-output (SISO) general linear node dynamics is directed and time invariant. Throughout this paper, the distributed control issue of multiagent systems is viewed and tackled as an output regulation problem and a distributed cooperative control law based on relative output measurements is proposed using classic pole assignment technique. Moreover, the notion of complex vector root locus (CVRL) is introduced, which is a generalization of classical root locus method, to analyze the stability of the control system.

Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint

This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.