In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix scaling weights. First, the algebraic properties of the matrix-scaled Laplacian and the geometry of the matrix-scaled consensus space are studied. Second, we examine matrix-scaled consensus algorithms for networks of single-integrators with or without constant parametric uncertainties. Nonlinear and finite-time matrix-scaled consensus algorithms are also proposed. Third, observer-based matrix-scaled consensus algorithms for homogeneous or heterogeneous linear-time invariant agents are designed. The convergence of the proposed algorithms is asserted by rigorous mathematical analysis and supported by numerical simulations.
Fully distributed consensus control for stochastic multi-agent systems under undirected and directed topologies
China University of Geosciences（中国地质大学）；Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems（复杂系统先进控制与智能自动化湖北省重点实验室）
In this paper, we first propose a novel maneuvering technique compatible with displacement-consensus-based formation controllers. We show that the formation can be translated with an arbitrary velocity by modifying the weights in the consensus Laplacian matrix. In fact, we demonstrate that the displacement-consensus-based formation control is a particular case of our more general method. We then uncover robustness issues with undesired steady-state motions and resultant distorted shapes in undirected displacement-consensus-based formation control. In particular, these issues are triggered when…
This paper presents the design and analysis of the finite/fixed-time scaled consensus for multiagent systems. A study on a generic attracting law, the certain classes of nonlinear systems that admit attractors with finite/fixed-time convergence, is at first given for the consensus purpose. The estimates for the lower and upper bounds on the settling time functions are provided through the two-phase analysis. The given estimates are initial state dependent, but the durations are finite, without regarding the values that the initial states take. According to the generic attracting law, distribut…
This paper proposes matrix-scaled consensus algorithm, which generalizes the scaled consensus algorithm in \cite{Roy2015scaled}. In (scalar) scaled consensus algorithms, the agents' states do not converge to a common value, but to different points along a straight line in the state space, which depends on the scaling factors and the initial states of the agents. In the matrix-scaled consensus algorithm, a positive/negative definite matrix weight is assigned to each agent. Each agent updates its state based on the product of the sum of relative matrix scaled states and the sign of the matrix we…
Consensus of autonomous agents is a benchmark problem in cooperative control. In this paper, we consider standard continuous-time averaging consensus policies (or Laplacian flows) over time-varying graphs and focus on robustness of consensus against communication delays. Such a robustness has been proved under the assumption of uniform quasi-strong connectivity of the graph. It is known, however, that the uniform connectivity is not necessary for consensus. For instance, in the case of undirected graph and undelayed communication consensus requires a much weaker condition of integral connectiv…
In this paper, we address two forms of consensus for multi-agent systems with undirected, signed, weighted, and connected communication graphs, under the assumption that the agents can be partitioned into three clusters, representing the decision classes on a given specific topic, for instance, the in favour, abstained and opponent agents. We will show that under some assumptions on the cooperative/antagonistic relationships among the agents, simple modifications of DeGroot's algorithm allow to achieve tripartite consensus(if the opinions of agents belonging to the same class all converge to t…
This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrix-weighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the time-varying network, necessary and/or sufficient conditions for which average consensus can be achieved are then provided in terms of the null space of matrix-valued Laplacian of the corresponding integral network. In particular, for periodic matrix-weighted time-varying networks, necessary and sufficient conditions for reaching average consensus is obtain…
The existing cryptosystem based approaches for privacy-preserving consensus of networked systems are usually limited to those with undirected topologies. This paper proposes a new privacy-preserving algorithm for networked systems with directed topologies to reach confidential consensus. As a prerequisite for applying the algorithm, a structural consensus problem is formulated and the solvability conditions are discussed for an explicitly constructed controller. The controller is then implemented with encryption to achieve consensus while avoiding individual's information leakage to external e…
Distributed estimation and control of node centrality in undirected asymmetric networks
Instituto de Investigación en Ingeniería de Aragón (I3A), Universidad de Zaragoza（阿拉贡工程研究所，萨拉戈萨大学）；Unit of Automatic Control, Department of Engineering, Università Campus Bio-Medico di Roma（罗马生物医学大学工程学院自动控制单元）；Department of Computer Science and Automation, University of “Roma Tre”（罗马第三大学计算机科学与自动化系）
Topological Controllability of Undirected Networks of Diffusively-Coupled Agents
Gwangju Institute of Science and Technology (GIST)（光州科学技术院）；Colorado School of Mines（科罗拉多矿业学院）；Korea Atomic Energy Research Institute（韩国原子能研究所）；Sunchon National University（顺天国立大学）
This work addresses the synchronization/consensus problem of identical multi-agent system (MAS) where the agents' dynamics are linear and the communication network is arbitrarily switching among connected topologies. The approach uses a gain matrix of a special structure in a dynamic compensator for each agent. Under reasonable conditions, the approach ensures that consensus is reached when the gain is sufficiently large. This result holds for general linear systems including the case where agents have repeated unstable eigenvalues. The proposed controller structure can be seen as a special ca…
This work shows an approach to achieve output consensus among heterogeneous agents in a multi-agent environment where each agent is subject to input constraints. The communication among agents is described by a time-varying directed/undirected graph. The approach is based on the well-known Internal Model Principle which uses an unstable reference system. One main contribution of this work is the characterization of the maximal constraint admissible invariant set (MCAI) for the combined agent-reference system. Typically, MCAI sets do not exist for unstable system. This work shows that for an im…
Institut de Matemàtica Multidisciplinària, Universitat Politècnica de València（多学科数学研究所，瓦伦西亚理工大学）；Departament de Sistemes Informàtics i Computació, Universitat Politècnica de València（信息系统与计算系，瓦伦西亚理工大学）
This paper investigates the consensus problem for nonlinear heterogeneous multi-agent systems with limited communication data rate. Each agent is modeled by a higher-order strict-feedback continuous-time system with unknown nonlinearities andexternal disturbance, and only the first state variable being measurable. Extended state observers (ESOs) are used to estimate the unmeasurable agent states and the unknown nonlinear dynamics. An ESO-based distributed output feedback protocol with dynamic encoding and decoding is then presented. It is shown that, for a connected undirected network, the pro…
Inspired and underpinned by the idea of integral feedback, a distributed constant gain algorithm is proposed for multi-agent networks to solve convex optimization problems with local linear constraints. Assuming agent interactions are modeled by an undirected graph, the algorithm is capable of achieving the optimum solution with an exponential convergence rate. Furthermore, inherited from the beneficial integral feedback, the proposed algorithm has attractive requirements on communication bandwidth and good robustness against disturbance. Both analytical proof and numerical simulations are pro…
This paper proposes model reduction approaches for consensus network systems based on a given clustering of the underlying graph. Namely, given a consensus network system of time-scaled agents evolving over a weighted undirected graph and a graph clustering, a parameterized reduced consensus network system is constructed with its edge weights and nodal time-scales as the parameters to be optimized. H-infinity- and H-2-based optimization approaches are proposed to select the reduced network parameters such that the corresponding approximation errors, i.e., the H-infinity- and H-2-norms of the e…
Existing Nussbaum function based methods on the consensus of multi-agent systems require (partial) identical unknown control directions of all agents and cause dangerous dramatic control shocks. This paper develops a novel saturated Nussbaum function to relax such limitations and proposes a Nussbaum function based control scheme for the consensus problem of multi-agent systems with arbitrary non-identical unknown control directions and safe control progress. First, a novel type of the Nussbaum function with different frequencies is proposed in the form of saturated time-elongation functions, w…
We propose a new decentralized average consensus algorithm with compressed communication that scales linearly with the network size n. We prove that the proposed method converges to the average of the initial values held locally by the agents of a network when agents are allowed to communicate with compressed messages. The proposed algorithm works for a broad class of compression operators (possibly biased), where agents interact over arbitrary static, undirected, and connected networks. We further present numerical experiments that confirm our theoretical results and illustrate the scalabilit…
Consensus of Multi-Agent Systems with General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols
School of Automation, Beijing Institute of Technology（北京理工大学自动化学院）；Department of Electrical and Computer Engineering, Utah State University（犹他州立大学电气与计算机工程系）
In this paper we study the influence of additive noise in randomized consensus algorithms. Assuming that the update matrices are symmetric, we derive a closed form expression for the mean square error induced by the noise, together with upper and lower bounds that are simpler to evaluate. Motivated by the study of Open Multi-Agent Systems, we concentrate on Randomly Induced Discretized Laplacians, a family of update matrices that are generated by sampling subgraphs of a large undirected graph. For these matrices, we express the bounds by using the eigenvalues of the Laplacian matrix of the und…
Average consensus is extensively used in distributed networks for computation and control, where all the agents constantly communicate with each other and update their states in order to reach an agreement. Under a general average consensus algorithm, information exchanged through wireless or wired communication networks could lead to the disclosure of sensitive and private information. In this paper, we propose a privacy-preserving push-sum approach for directed networks that can protect the privacy of all agents while achieving average consensus simultaneously. Each node decomposes its initi…
In this brief paper, a new consensus protocol based on the sign of innovations is proposed. Based on this protocol each agent only requires single-bit of information about its relative state to its neighboring agents. This is significant in real-time applications, since it requires less computation and/or communication load on agents. Using Lyapunov stability theorem the convergence is proved for networks having a spanning tree. Further, the convergence is shown to be in finite-time, which is significant as compared to most asymptotic protocols in the literature. Time-variant network topologie…
This paper investigates the distributed event-based consensus problem of switching networks satisfying the jointly connected condition. Both the state consensus of homogeneous linear networks and output consensus of heterogeneous networks are studied. Two kinds of event-based protocols based on local sampled information are designed, without the need to solve any matrix equation or inequality. Theoretical analysis indicates that the proposed event-based protocols guarantee the achievement of consensus and the exclusion of Zeno behaviors for jointly connected undirected switching graphs. These …
In this paper, we develop and analyze a gossip-based average consensus algorithm that enables all of the components of a distributed system, each with some initial value, to reach (approximate) average consensus on their initial values after executing a finite number of iterations, and without having to reveal the specific value they contribute to the average calculation. We consider a fully-connected (undirected) network in which each pair of components (nodes) can be randomly selected to perform pairwise standard gossip averaging of their values, and propose an enhancement that can be follow…
Fully Distributed Adaptive Consensus Approach for Economic Dispatch Problem
Vidya Pratishthan’s Kamalnayan Bajaj Institute of Engineering & Technology（Vidya Pratishthan's Kamalnayan Bajaj 工程与技术学院）；IIT Delhi（德里印度理工学院）；National Institute of Technology Rourkela（鲁尔克拉国家技术学院）
