Control Of Multi-agent Networks Research Articles

Fully Distributed Control of Multiagent Networks With Edge-Based Event-Triggered Communication

This paper addresses the synchronization problem of linear multi-agent systems with intermittent communication. To solve this problem, we propose an adaptive distributed control algorithm with edge-based event-triggering mechanisms that differs fundamentally from existing approaches in that it does not employ any form of global topology information and absolute state information. Instead, agents update their control signals and check triggering conditions based on relative state information. As our main contribution, we prove that all agents achieve global asymptotic synchronization with strictly positive minimum inter-event times by using the proposed event-triggered control method when the communication graph is connected. The main result is illustrated with an example, and through which we demonstrate the effectiveness of the proposed algorithm.

Two-Level Control of Multiagent Networks for Dynamic Coverage Problems.

We propose a two-level coverage control framework for a multiagent network whose members have to deploy over a given region in accordance with a (possibly time-varying) coverage density function. Our approach is based on a two-level description of the multiagent network. The first level corresponds to the probability density function of the agents' locations over a given region, in which the multiagent network is treated as one unit (macroscopic description), whereas in the second level, the network is described in terms of the collection of all individual positions of its agents (microscopic description). The goal of the multiagent network is to attain a spatial distribution that (approximately) matches the reference coverage density function (high-level coverage control problem) through local interactions of the agents of the network at the individual level (low-level coverage control problem). We address the high-level control problem by associating it with an interpolation problem in the class of Gaussian mixtures. Furthermore, we address the low-level control problem by utilizing a variation of Lloyd's algorithm with a time-varying coverage density function, which is updated at each step based on the distribution of the agents' locations. Because the high-level and the low-level coverage control problems are inherently coupled to each other, we propose an iterative scheme that combines their solutions in order to address the deployment problem in a holistic way. Finally, a set of simulation results is provided to show the effectiveness of the proposed approach.

Controllability of consensus heterogeneous multi-agent networks over continuous time scale

Abstract The research, presented in this paper, concernes the controllability of a multi-agent network with a directed, unweighted, cooperative, and time-invariant communication topology. The network’s agents follow linear and heterogeneous dynamics, encompassing first-order, second-order, and third-order differential equations over continuous time. Two classes of neighbour-based linear distributed control protocols are considered: the first one utilises average feedback from relative velocities/relative accelerations, and the second one utilises feedback from absolute velocities/absolute accelerations. Under both protocols, the network’s agents achieve consensus in their states asymptotically. We observe that both of the considered dynamical rules exploit the random-walk normalised Laplacian matrix of the network’s graph. By categorising the agents of the network into leaders and followers, with leaders serving as exogenous control inputs, we analyse the controllability of followers within their state space through the influence of leaders. Specifically, matrix-rank conditions are established to evaluate the leader–follower controllability of the network under both control protocols. These matrix-rank conditions are further refined in terms of the system matrices’ eigenvalues and eigenvectors. The inference diagrams presented in this work provide deeper insights into how leader–follower interactions impact the network controllability. The efficacy of the theoretical findings is validated through numerical examples.

Formation Control of Multiagent Networks: Cooperative and Antagonistic Interactions

This article studies the formation control problem of second-order multiagent networks, in which cooperative and antagonistic interactions of the agents spontaneously coexist in the communication process. Based on the convex analysis theory, several convex polytopes that do not require some kinds of system constraints are constructed in the presence of these interactions. Then, the matrix perturbation theory and some mathematical techniques are utilized to analyze these convex polytopes. The obtained results show that the agents with cooperative interactions monotonously converge to their own specified formation shape while maintaining the desired relative position of the other agents with antagonistic interactions. Subsequently, two numerical examples are presented to illustrate the obtained results.

On the Selection of Leaders for the Controllability of Multi-agent Networks

On the Selection of Leaders for the Controllability of Multi-agent Networks

Control of multiagent networks with misbehaving nodes

ABSTRACT We study multiagent networks with floating, driver, and unmodelled nodes, where floating nodes exchange local information, driver nodes not only exchange local information but also take input and output roles, and unmodelled nodes have an unknown but bounded behaviour. Specifically, we consider the presence of misbehaving nodes within the floating and driver nodes in addition to the misbehaviours resulting from the unmodelled nodes, and propose a feedback control approach applied to the driver nodes for suppressing the effect of all misbehaving nodes in the multiagent network. We show closed-loop stability with the proposed approach, where the driver nodes asymptotically or closely follow a given command and the remaining nodes may also follow this command or remain bounded depending on the location of driver nodes in the multiagent network. Considering limited resources in that the number of driver nodes is generally fewer than the number of floating nodes, we further characterize the effect of the location of the driver nodes to closed-loop stability. Our findings reveal how the driver nodes need to be selected for isolating the effect of misbehaving nodes in certain portions of the multiagent network such that the nodes in those portions also follow the given command.

Model-matching methods and distributed control of networks consisting of a class of heterogeneous dynamic agents

Many recent results on distributed control of multi-agent networks rely on a number of simplifying assumptions that facilitate the solution of regulation problems associated with large-scale networked systems. Identical subsystem models are a typical assumption made in networked control systems which often fail in practice. In this paper, we propose a systematic method for removing this assumption, leading to a general approach to distributed-control design for stabilising networks of multiple non-identical dynamic agents. Local subsystems represented as autonomous dynamic agents are assumed to share a set of structural properties, (controllability) indices. Our approach relies on the solution of certain model-matching type problems using local state-feedback and state/input-matrix transformations that map local dynamics to a target system, selected to minimise joint control effort. By adapting well-established distributed LQR control design methodologies to our framework, the stabilisation problem of networks of non-identical dynamic agents is solved. The applicability of our approach is illustrated via a synchronisation example of eleven harmonic oscillators with non-identical dynamics communicating over a connected graph.

Structural Controllability of Directed Signed Networks

In this article, the structural controllability of multiagent networks defined over directed signed graphs is investigated, where the agents are divided into leaders and followers, and only leaders are manipulated by the external control input directly. The communication digraph contains positive and negative edges, which represent cooperative and antagonistic interactions between agents, respectively. First, a graph-theoretic necessary and sufficient condition for structural controllability of multiagent networks is derived, that is, a multiagent network is structurally controllable if and only if the communication digraph is leader–follower connected. Next, the minimal controllability problem is studied. It is shown that the minimal controllability problem is solvable, and a method of polynomial complexity to accomplish minimal structural controllability is developed. In addition, the structural controllability of specified Cartesian product networks is discussed and a necessary and sufficient condition concerning the factor networks for the structural controllability is established. The application of the theoretical results is demonstrated by several practical examples.

Finite-horizon robust formation-containment control of multi-agent networks with unknown dynamics

In the paper, data-driven finite-horizon robust formation-containment control scheme is developed based on integral reinforcement learning and zero-sum game for perturbed multi-agent networks with completely unknown nonlinear dynamics. At first, distributed finite-time sliding mode estimators are designed to obtain the desired states of leaders and followers, respectively. Then finite-horizon robust leader formation control and follower containment control are achieved based on proposed model-free integral reinforcement learning algorithms implemented by critic-actor-disturbance structure, in the framework of multi-player zero-sum game where the non-quadratic performance index for each agent considers the influence of saturated inputs and disturbances of local neighbors thoroughly. Furthermore, it is proved that the whole network has bounded L2 gain robust stability and Nash equilibrium of zero-sum game exists. Simulation results are provided to demonstrate the effectiveness of the proposed scheme.

Finite-time control of multiagent networks as systems with time transformation and separation principle

In this paper, we study finite-time control of multiagent networks as systems, where they involve floating agents that exchange local information and driver agents that not only exchange local information but also take input and output roles. For this class of multiagent networks, control algorithms are applied to the driver agents based on the measurements collected from them for the purpose of influencing the overall behavior of the resulting system. Specifically, we consider time-critical applications in the control of multiagent networks as systems and propose a finite-time control approach predicated on a recent time transformation method. The proposed method guarantees execution of control algorithms over a prescribed time interval [0,T) with T being a user-defined convergence time based on analysis performed over a stretched, infinite-time interval [0,∞). We analytically show that the resulting system achieves user-defined finite-time convergence regardless of the initial conditions of agents, where we also discuss the separation principle obtained with the proposed method. The presented theoretical contributions are not only illustrated by numerical examples but also experimentally validated using ground mobile robots.

Distributed Coverage Control of Multi-Agent Networks with Guaranteed Collision Avoidance in Cluttered Environments

We propose a distributed control algorithm for a multi-agent network whose agents deploy over a cluttered region in accordance with a time-varying coverage density function while avoiding collisions with all obstacles they encounter. Our algorithm is built on a two-level characterization of the network. The first level treats the multi-agent network as a whole based on the distribution of the locations of its agents over the spatial domain. In the second level, the network is described in terms of the individual positions of its agents. The aim of the multi-agent network is to attain a spatial distribution that resembles that of a reference coverage density function (high-level problem) by means of local (microscopic) interactions of its agents (low-level problem). In addition, as the agents deploy, they must avoid collisions with all the obstacles in the region at all times. Our approach utilizes a modified version of Voronoi tessellations which are comprised of what we refer to as Obstacle-Aware Voronoi Cells (OAVC) in order to enable coverage control while ensuring obstacle avoidance. We consider two control problems. The first problem which we refer to as the high-level coverage control problem corresponds to an interpolation problem in the class of Gaussian mixtures (no collision avoidance requirement), which we solve analytically. The second problem which we refer to as the low-level coverage control problem corresponds to a distributed control problem (collision avoidance requirement is now enforced at all times) which is solved by utilizing Lloyd's algorithm together with the modified Voronoi tessellation (OAVC) and a time-varying coverage density function which corresponds to the solution of the high-level coverage control problem. Finally, simulation results for coverage in a cluttered environment are provided to demonstrate the efficacy of the proposed approach.

Cooperative control for cyber–physical multi-agent networked control systems with unknown false data-injection and replay cyber-attacks

The paper discusses the cooperative tracking problem of partially known cyber–physical multi-agent networked systems. In this system, there exist two cascaded chances for cyber-attacks. The local agent is of networked system type that is subjected to unknown false data-injection and replay cyber-attacks that are dissimilar in the sensor-controller and the controller-actuator network parts. The communication between any two agents, if they are connected, is accomplished via a communication network that is subjected to false data-injection cyber-attacks. The problem of the existing two cascaded chances for cyber-attacks is solved in three steps. First, with partially known system parameters and unknown false data-injection and replay cyber-attacks, the state estimates of all the local followers are evaluated by designing local adaptive observers. Second, a new technique is designed to compensate for the unmatched terms that result from the use of local adaptive observers. After that, distributed adaptive leader–follower security controllers are proposed based on the local estimated information in addition to the infected arrived information from the neighbors. Meanwhile, it is verified that the suggested security control method guarantees that all states of the followers under the considered cyber-attacks follow the given leader asymptotically. The efficacy of the developed adaptive leader–follower security controllers is verified via an illustrative example.

Distributed adaptive switching control of uncertain switched affine multi-agent systems

In this paper, motivated by the need for distributed control of multi-agent networks consist of switched affine systems, a distributed leader following consensus controller is developed. Different from most existing methods with affine control multi-agent systems, switched affine multi-agent systems face additional difficulties in the analysis and control, meanwhile affine diffusive coupling consensus algorithms are not applicable. So, in this paper switching signal is considered as the only control mechanism. Two consensus algorithms are proposed based on min-switching control and a new distributed embedded pulse width modulation (PWM) technique, in which local and neighbors output feedback are used to construct control input via an adaptive observer. Proposed observer-based distributed adaptive switching strategies guarantee stability of the overall network in the presence of uncertain affine term. Finally, proposed distributed control algorithms are verified by simulation of a switched affine multi-agent system.

Controllability of Multiagent Networks With Antagonistic Interactions

This paper addresses the controllability of a class of antagonistic multiagent networks with both positive and negative edges. All the agents of the multiagent network run a consensus algorithm using a signed Laplacian. Based on the generalized equitable partition, we propose a graph-theoretic characterization of an upper bound on the controllable subspace. Then, we provide a necessary condition for the controllability of the system and give an algorithm to compute the partition. Furthermore, we prove that for a structurally balanced network, the controllability is equivalent to that of the corresponding all-positive network, if the leaders are chosen from the same vertex set. Several examples are given to illustrate these results.

JLS-PPC: A Jump Linear System Framework for Networked Control

We present a unified formalism for multiagent networked control and estimation with scheduling, delays, and packet loss in the communication channels between the controller and distributed sensors and actuators. The modular framework is a combined construction of a stochastic jump linear system (JLS) description of the plant and network effects, a Kalman filter-based estimator, and packetized predictive control, a receding horizon optimization technique with buffering at the actuator. Integration of these elements enables the synthesis of a novel estimation technique that generalizes prior approaches for control and measurement packet loss to the case with schedules, delays, control buffering, and most importantly, delayed and lossy control packet acknowledgments (ACKs). The JLS framework allows a clean separation of jump variable estimation and a posteriori state estimation using a backup-and-rerun strategy, and can handle variable-length ACK histories for multiple independent control communication channels. Finally, we derive modified covariance priors for the filter that account for uncertainty in the control action applied at the vehicle when ACKs are not available and control buffers are used. Simulations with single vehicle and multivehicle systems demonstrate the methods and show the benefits of utilizing delayed and lossy ACKs.

Almost equitable partitions and new necessary conditions for network controllability

In this paper, we consider the controllability problem for multi-agent networked control systems. The main results of the paper are new graph-theoretic necessary conditions for controllability involving almost equitable graph vertex partitions. We generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple-leaders and we also consider the broadcasted control scenario. Our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number-theoretic properties of the communities. We show via examples that our results can be used to account for a large portion of uncontrollable inducing leader-selections that could not have otherwise been accounted for using symmetry results.

Event-Triggering Containment Control for a Class of Multi-Agent Networks With Fixed and Switching Topologies

This paper investigates the event-triggering containment control of multi-agent networks with fixed and switching topologies, where there exist interactions between the leaders. Two cases are studied, respectively: One is that the leaders are opinionated. Then each leader will converge to its initial goal and the followers converge to the convex hull formed by the leaders. The other is that the leaders are not opinionated. Then the leaders will not insist on their initial goals and converge to some compromising states due to the interactions among them, while the followers still converge to the convex hull formed by the leaders. By means of pull-based event-triggering control, the event-triggering containment control problems of multi-agent systems with fixed and switching topologies are investigated, respectively. Finally, simulations are given to illustrate the theoretical results.

Group controllability of discrete-time multi-agent systems

Controllability is a fundamental issue concerning control of multi-agent networks and a very important research topic in the modeling, analysis and coordination control of multi-agent systems. Group controllability problem is a further extension of the controllability problem of the general multi-agent systems, which mainly studies the cooperation and control of multi-agent systems with multiple sub-groups or multiple intelligence clusters. Comparing with the controllability of the general multi-agent systems, the group controllability is not only to consider the information interaction among the groups, but also to consider the information interaction between different groups, which makes the system reflect the effect of a whole and also the internal structure of the sub-groups. This paper addresses the group controllability problems of discrete-time multi-agent systems with time-delay, in which both switching topology and fixed topology are considered. This paper also proposes the general definition of the group controllability, as well as establishes group controllability criteria from the algebraic and graphical perspectives. Numerical examples and simulations are proposed to illustrate the theoretical results.

High-Performance Consensus Control in Networked Systems With Limited Bandwidth Communication and Time-Varying Directed Topologies.

Communication data rates and energy constraints are two important factors that have to be considered in the coordination control of multiagent networks. Although some encoder-decoder-based consensus protocols are available, there still exists a fundamental theoretical problem: how can we further reduce the update rate of control input for each agent without the changing consensus performance? In this paper, we consider the problem of average consensus over directed and time-varying digital networks of discrete-time first-order multiagent systems with limited communication data transmission rates. Each agent has a real-valued state but can only exchange binary symbolic sequence with its neighbors due to bandwidth constraints. A class of novel event-triggered dynamic encoding and decoding algorithms is proposed, based on which a kind of consensus protocol is presented. Moreover, we develop a scheme to select the numbers of time-varying quantization levels for each connected communication channel in the time-varying directed topologies at each time step. The analytical relation among system and network parameters is characterized explicitly. It is shown that the asymptotic convergence rate is related to the scale of the network, the number of quantization levels, the system parameter, and the network structure. It is also found that under the designed event-triggered protocol, for a directed and time-varying digital network, which uniformly contains a spanning tree over a time interval, the average consensus can be achieved with an exponential convergence rate based on merely 1-b information exchange between each pair of adjacent agents at each time step.

Consensus Control for Variable Multi-Agent Systems with Faults and Disturbances

This paper investigates multi-agent consensus problem with an active leader as well as external disturbances and some faults. The undirected networks with variable interconnection topology are taken into consideration. Distributed consensus control algorithm is proposed to analyze the disturbance rejection and fault sensitivity problem arising in the coordination control of multi-agent networks. With a proposed control scheme, we then present sufficient conditions under which all agents can reach consensus with the desired performance index. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results.