This paper addresses the distributed prescribed-time leader-following consensus problem for a class of high-order multi-agent systems (MASs) with perturbed nonlinear agents dynamics and where the topology of the network contains a directed spanning tree, with the leader as the root. Prescribed-time consensus means that an agreement state of the MAS is achieved in a preset time, introduced as a parameter of the control law, and this constant settling time is achieved independently of the agents' initial state. The proposed control method exhibits three main advantages: first, to our best knowledge, it is the first time that prescribed-time convergence in a consensus problem is achieved for agents with high-order nonlinear dynamics, using a robust leader-following protocol, which allows an effective rejection of matched disturbances in the agents' model. Second, the proposed controller provides control signals of lower magnitude than existing approaches. Third, the proposed consensus protocol does not have parameters to be adjusted depending on the connectivity of the considered communication graph.
This paper presents new classes of consensus protocols with fixed-time convergence, which enable the definition of an upper bound for consensus state as a parameter of the consensus protocol, ensuring its independence from the initial condition of the nodes. We demonstrate that our methodology subsumes current classes of fixed-time consensus protocols that are based on homogeneous in the bi-limit vector fields. Moreover, the proposed framework enables for the development of independent consensus protocols that are not needed to be homogeneous in the bi-limit. This proposal offers extra degrees…
We propose predefined-time consensus-based cooperative guidance laws for a swarm of interceptors to simultaneously capture a target capable of executing various kinds of motions. Unlike leader-follower cooperative guidance techniques, the swarm of interceptors has no leader and each interceptor executes its own guidance command in a distributive fashion, thus obviating the residency of the mission over a single interceptor. We first design cooperative guidance commands subject to target's mobility, followed by the same when the target is stationary, and also account for interceptors' changing …
This paper addresses the robust consensus problem under switching topologies. Contrary to existing methods, the proposed approach provides decentralized protocols that achieve consensus for networked multi-agent systems in a predefined time. Namely, the protocol design provides a tuning parameter that allows setting the convergence time of the agents to a consensus state. An appropriate Lyapunov analysis exposes the capability of the current proposal to achieve predefined-time consensus over switching topologies despite the presence of bounded perturbations. Finally, the paper presents a compa…
This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distributed optimization problem. To solve this problem, we first augment each agent with an optimal signal generator to reproduce the global optimal point of the given distributed optimization problem, and then complete the global optimal consensus design by developing some adaptive tracking controllers for these augmented agents. Moreover, we present an e…
This paper is concerned with the consensus problem for multi-agent systems subject to communication delays between the neighboring agents. We consider a scenario where each agent is characterized by a general high-order linear system and the communication delays between the agents are non-uniform and time-varying. We design a distributed control protocol for the agents and provide an equivalent stability problem to be solved that guarantees the state consensus in the group of agents. Moreover, a delay-dependent stability criterion is provided by combining the Lyapunov-Krasovskii method with th…
This paper focuses on the problem of distributed consensus control of multi-agent systems while considering two main practical concerns (i) stochastic noise in the agent dynamics and (ii) predefined performance constraints over evolutions of multi-agent systems. In particular, we consider that each agent is driven by a stochastic differential equation with state-dependent noise which makes the considered problem more challenging compared to non-stochastic agents. The work provides sufficient conditions under which the proposed timevarying distributed control laws ensure consensus in expectatio…
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…
The distributed optimal output consensus problem for high-order multi-agent systems has been studied recently. In this paper, we further focus on the same problem for high-order multi-agent systems subject to parametric uncertainties and aim at distributed robust controllers by measurement output feedback. We first develop a dynamic compensator to estimate the expected optimal consensus point and convert the problem into several decentralized robust tracking problems. Then, by combining the integral control technique and dirty derivative observer technique, we constructively propose a distribu…
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）
Optimal Output Consensus of High-Order Multi-Agent Systems with Embedded Technique
Beijing University of Posts and Telecommunications（北京邮电大学）；Central South University（中南大学）；Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）
Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics
School of Automation, Beijing Institute of Technology（北京理工大学自动化学院）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）
In this paper, we consider the privacy preservation problem in both discrete- and continuous-time average consensus algorithms with strongly connected and balanced graphs, against either internal honest-but-curious agents or external eavesdroppers. A novel algorithm is proposed, which adds edge-based perturbation signals to the process of consensus computation. Our algorithm can be divided into two phases: a coordinated scrambling phase, which is for privacy preservation, and a convergence phase. In the scrambling phase, each agent is required to generate some perturbation signals and add them…
Leader-following Consensus of Multi-agent Systems over Finite Fields
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院系统与控制中心）；Chinese Academy of Sciences（中国科学院）
Some of the issues associated with the practical applications of consensus of multi-agent systems (MAS) include switching topologies, attrition and inclusion of agents from an existing network, and model uncertainties of agents. In this paper, a single distributed dynamic state-feedback protocol referred to as the Robust Attrition-Inclusion Distributed Dynamic (RAIDD) consensus protocol, is synthesized for achieving the consensus of MAS with attrition and inclusion of linear time-invariant higher-order uncertain homogeneous agents and switching topologies. A state consensus problem termed as t…
This paper presents the distributed pinning consensus solution for nonlinear positive multi-agent systems with nonlinear control input by applying observer-based control protocols. The network topology is considered as a directed and fully connected structure. By considering sector input nonlinearities and various forms of topologies, two kinds of state observers involving standard observer and distributed pinning observer are presented for each regarded nonlinear agent by applying a novel analysis directly dealing with the nonlinear input and nonlinear system dynamics. The measured local outp…
In this note, the problem of simultaneous leader-following consensus and parameter estimation is studied for a class of multi-agent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies and phases. A distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adap…
Exploiting the Superposition Property of Wireless Communication for Max-Consensus Problems in Multi-Agent Systems
Technische Universität Berlin（柏林工业大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）；Max-Planck-Institut für Dynamik komplexer technischer Systeme（复杂技术系统动力学马普研究所）
This brief addresses the distributed consensus problem of nonlinear multi-agent systems under a general directed communication topology. Each agent is governed by higher-order dynamics with mismatched uncertainties, multiple completely unknown high-frequency gains, and external disturbances. The main contribution of this brief is to present a new distributed consensus algorithm, enabling the control input of each agent to require minimal information from its neighboring agents, that is, only their output information. To this end, a dynamic system is explicitly constructed for each agent to gen…
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…
In this paper we address the consensus problem in the context of networked agents whose communication graph can be split into a certain number of clusters in such a way that interactions between agents in the same clusters are cooperative, while interactions between agents belonging to different clusters are antagonistic. This problem set-up arises in the context of social networks and opinion dynamics, where reaching consensus means that the opinions of the agents in the same cluster converge to the same decision. The consensus problem is here investigated under the assumption that agents in …
In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are est…
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…
Time-varying hierarchical multi-agent systems are common in many applications. A well-known solution to control these systems is to use state feedback controllers that depend on the adjacency matrix to reach consensus. This solution has been applied so far to multi-agent systems with fixed or time-varying communication topologies. In this paper, we consider single-integrator multi-agent systems where only a subset of the agents are active at any given time and the set of active agents is time-varying. This type of multi-agent system is relevant in applications such as modular multilevel conver…
In this paper we investigate the problem of the sudden disconnection of an edge in a discrete-time multi-agent consensus network. If the graph remains strongly connected, the multi-agent system still achieves consensus, but in general, unless the information exchange between each pair of agents is symmetric, the agents' states converge to a drifted value of the original consensus value. Consequently the edge disconnection can go unnoticed. In this paper the problems of detecting an edge disconnection and of identifying in a finite number of steps the exact edge that got disconnected are invest…
On Non-Consensus Motions of Dynamical Linear Multi-Agent Systems
Northwest University for Nationalities（西北民族大学）；Key Laboratory of National Language Intelligent Processing, Gansu Province（甘肃省国家语言智能处理重点实验室）；Huazhong University of Science and Technology（华中科技大学）；Hangzhou Dianzi University（杭州电子科技大学）
This paper studies a consensus problem of multi-agent systems subjected to external disturbances over the clustered network. It considers that the agents are divided into several clusters. They are almost all the time isolated one from another, which has a directed spanning tree. The goal of agents achieves a common value. To support interaction between clusters with a minimum exchange of information, we consider that each cluster has an agent, who can exchange information to any agents outside of its cluster at some discrete instants of time. Our main contribution proposes a consensus protoco…
Group consensus implies reaching multiple groups where agents belonging to the same cluster reach state consensus. This paper focuses on linear multi-agent systems under nonnegative directed graphs. A new necessary and sufficient condition for ensuring group consensus is derived, which requires the spanning forest of the underlying directed graph and that of its quotient graph induced with respect to a clustering partition to contain equal minimum number of directed trees. This condition is further shown to be equivalent to containing cluster spanning trees, a commonly used topology for the un…
Achieving average consensus without disclosing sensitive information can be a critical concern for multi-agent coordination. This paper examines privacy-preserving average consensus (PPAC) for vector-valued multi-agent networks. In particular, a set of agents with vector-valued states aim to collaboratively reach an exact average consensus of their initial states, while each agent's initial state cannot be disclosed to other agents. We show that the vector-valued PPAC problem can be solved via associated matrix-weighted networks with the higher-dimensional agent state. Specifically, a novel di…
This paper studies the optimal output consensus problem for a group of heterogeneous linear multi-agent systems. Different from existing results, we aim at effective controllers for these high-order agents under both event-triggered control and event-triggered communication settings. We conduct an embedded design for the problem and constructively propose a multi-rate event-triggered controller with a set of applicable parameters. The proposed event-triggered rules are shown to be free of Zeno behaviors and can achieve the optimal output consensus goal for these high-order agents. A simulation…
This paper studies the consensus problem of general linear discrete-time multi-agent systems (MAS) with input constraints and bounded time-varying communication delays. We propose a robust distributed model predictive control (DMPC) consensus protocol that integrates the offline consensus design with online DMPC optimization to exploit their respective advantages. More precisely, each agent is equipped with an offline consensus protocol, which is a priori designed, depending on its immediate neighbors' estimated states. Further, the estimation errors propagated over time due to inexact neighbo…
