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While applying control signals to every node is typically considered in multiagent networks to mitigate the adverse effects of misbehaving nodes, this control strategy may not always be possible due to physical constraints and/or economical limitations. Motivated by this standpoint, we have recently focused on how to control misbehaving multiagent networks through sending control signals to a subset of nodes (i.e. driver nodes) for suppressing the adverse effects of misbehaving nodes in the overall multiagent network, where the driver nodes only use their own state information to generate their control signals. To address the open problem where the driver nodes cannot obtain their own state information, the main contribution of this paper is that we now take into account that these nodes need to generate their control signals using the state information received from other subset of nodes (i.e. observer nodes). We characterise which nodes in the network behave as desired based on the selection of driver nodes and observer nodes in control of misbehaving multiagent networks. In addition, we provide numerical examples to illustrate the effectiveness of the proposed approach as well as the importance of the selection of driver and observer nodes for maximising the number of nodes that exhibit the desired responses. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed average-tracking (DAT) problem of multiagent networks (MANs) with same input delay under an undirected topology. A distributed fixed-time average-tracking algorithm driven by an event-triggered method is constructed to ensure the agents reach the average value of multiple time-varying reference input signals (TVRISs) within the fixed time. By using Lyapunov function method, sufficient conditions on estimating the fixed settling time and the bounded average-tracking errors are obtained. In addition, it is proved that the event-triggered control strategy avoids the Zeno behavior. Finally, a few numerical simulations are given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The graph properties of r - and (r , s)-robustness are of importance for multiagent networks since these properties ensure consensus among agents even in the presence of a limited number of arbitrarily misbehaving agents, given sufficiently large values for the integers r and s. However, determining the exact solutions of r - and (r , s)-robustness of an arbitrary directed graph has been proven to be computationally complex NP-hard problem. In this paper, we introduce a novel method, named the Determining Robustness based Genetic Algorithm (DRSGA), for approximately calculating the r - and (r , s)-robustness using heuristic algorithm. According to graph theory in mathematical analysis, we first formalize the method for calculating the r - and (r , s)-robustness in directed graphs by utilizing a three-vertex set partition. Then, we transform these methods into a minimization problem of an n -dimensional discrete function and employ DRSGA to obtain an approximate solution. Finally, we validate the efficacy of our algorithm through a series of experiments compared to existing mixed-integer programming algorithms. [ABSTRACT FROM AUTHOR]

This article studies the consensus and the input delay compensation problems for discrete‐time linear multiagent networks with time delays in the state and input. Pseudo‐predictor feedback (PPF) protocol is proposed, which makes use of the artificial closed‐loop dynamics to predict the future states. Sufficient conditions are offered to guarantee the multiagent consensus on the grounds of the stability of difference equations. Full‐order observer based PPF protocol and reduced‐order observer based PPF protocol are simultaneously established, and it is revealed that, under the PPF protocol, the convergence rate of the states is fastest. Compared with the existent predictor feedback protocol, the proposed protocol greatly reduces the calculation burden and is easier to implement since it has no concern with the (history) input information. Finally, a numerical example is carried out to demonstrate the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

The constraints of communication channel resources and control energies always lie in real networks, which bring large error and cause adverse affects on system performance, ultimately. To address these limitations, in this article, a distributed event-triggered impulsive control strategy for the consensus problem of fractional-order multiagent networks (FOMANs) is investigated. By collecting the local instantaneous access information, the distributed tracking algorithm with a novel triggering condition is proposed, which is available for both linear and nonlinear systems. Combining with general quadratic Lyapunov stability method and discontinuous control theory, the sufficient conditions of consensus in terms of gain parameter and impulsive interval are derived. Furthermore, the minimal length of interevent is proven to be strictly greater than zero, which guarantees the nonexistence of Zeno-behavior in the closed-loop system. In addition, the implementation of the fractional order algorithm, the quantitative relationship between fractional order $\alpha $ or parameter $a$ in the triggering function, and the number of event-triggered impulsive instants are discussed. At the end of this article, two illustrative examples with numerical and circuit simulations are provided to validate the effectiveness of above results. [ABSTRACT FROM AUTHOR]

In this article, the problem of distributed generalized Nash equilibrium (GNE) seeking in noncooperative games is investigated via multiagent networks, where each player aims to minimize his or her own cost function with a nonsmooth term. Each player’s cost function and feasible action set in the noncooperative game are both determined by actions of others who may not be neighbors, as well as his/her own action. Particularly, feasible action sets are constrained by private convex inequalities and shared linear equations. Each player can only have access to his or her own cost function, private constraint, and a local block of shared constraints, and can only communicate with his or her neighbours via a digraph. To address this problem, a novel continuous-time distributed primal–dual algorithm involving Clarke’s generalized gradient is proposed based on consensus algorithms and the primal–dual algorithm. Under mild assumptions on cost functions and graph, we prove that players’ actions asymptotically converge to a GNE. Finally, a simulation is presented to demonstrate the effectiveness of our theoretical results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article investigates the synthesis of distributed economic control algorithms under which dynamically coupled physical systems are regulated to a variational equilibrium of a constrained convex game. We study two complementary cases: 1) each subsystem is linear and controllable and 2) each subsystem is nonlinear and in the strict-feedback form. The convergence of the proposed algorithms is guaranteed using the Lyapunov analysis. Their performance is verified by two case studies on a multizone building temperature regulation problem and an optimal power flow problem, respectively. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to investigate the consensus of linear multiagent networks with time-varying characteristics under sampled-data communications, where the time-varying characteristics include both time-varying topologies and the node’s linear time-varying dynamics. By using the decoupling method, we prove that the sampled-data consensus problem of multiagent networks is equal to the stability problem of sampled-data systems. Then, the globally asymptotical consensus is investigated for multiagent networks with time-varying characteristics by virtue of the Lyapunov function method. It should be noted that when the Lyapunov function method is utilized to investigate the stability problem of control systems, it is always assumed that the derivative of the constructed Lyapunov function is not more than zero. This assumption is removed here and as a replacement, the average value of the derivative of the Lyapunov function in a period to be negative is needed. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the output synchronization of a group of heterogeneous agents with nonlinear dynamics. It is shown that via dynamic coupling, the output synchronization problem is transformed into a family of output homogenization and internal-model-based synchronization problems. In contrast to conventional approaches, the adopted approach does not rely on the generation of a specific reference trajectory, to be tracked by all agents. Based on this premise, we propose a distributed state-feedback protocol driving all the heterogeneous multiagent individual systems onto a copy of a virtual reference signal. Invoking the results from the theory of output regulation and cooperative control, the state-feedback controller synthesis is conducted to achieve the output synchronization of heterogeneous multiagent networks. Immediate extensions of the obtained results to observer-based control are also discussed. The effectiveness of the proposed output synchronization algorithm is verified through theoretical analysis and case studies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper focuses on studying the differentially private consensus problem in multiagent networks under a quantized communication environment, where the exact real-value state is not available for transmission due to the range limitation of digital channels. We first extend the differentially private consensus model to the case of a quantized communication environment integrated with a dynamic encoding/decoding scheme and propose a differentially private communication algorithm utilizing the quantized state with a bounded quantizer instead of the exact real-value state to reach an agreement while protecting the initial or current states of the participants from information disclosure. Then, the convergence analysis of mean square consensus in the case of an unbounded quantizer is given to explain the sufficiency of the extended model and convergence conditions. To overcome the uncertainty of saturation in the case of a bounded quantizer, we also give a statistical analysis on the boundedness of quantization that the bounded quantizer with a finite number of bits can remain unsaturated with a desired high probability under certain conditions. Furthermore, we provide the statistical analysis on the convergent accuracy, which shows that the agreement value just converges to a random variable that falls in the neighboring range of the initial state average and the expectation of the agreement value is equal to the initial state average exactly. In addition, we provide the differential privacy analysis for individual agents and the whole network, and then establish the potential relationship between the dynamic encoding/decoding scheme and the differential privacy mechanism. Finally, the simulation results visually show that the proposed algorithm and the main theoretical results are effective and correct. [ABSTRACT FROM AUTHOR]

A distributed nonsmooth convex optimization problem subject to a general type of constraint, including equality and inequality as well as bounded constraints, is studied in this paper for a multiagent network with a fixed and connected communication topology. To collectively solve such a complex optimization problem, primal–dual dynamics with projection operation are investigated under optimal conditions. For the nonsmooth convex optimization problem, a framework under the LaSalle’s invariance principle from nonsmooth analysis is established, where the asymptotic stability of the primal–dual dynamics at an optimal solution is guaranteed. For the case where inequality and bounded constraints are not involved and the objective function is twice differentiable and strongly convex, the globally exponential convergence of the primal–dual dynamics is established. Finally, two simulations are provided to verify and visualize the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents the impulsive average quasi-consensus algorithm for distributed constrained convex optimization. First, the constrained optimization problem can be transformed into an unconstrained problem using the interior point method, and then a distributed algorithm is modeled by means of impulsive differential equation. In the framework of the continuous-time gradient method and algebraic graph theory, each agent can deal with one local objective function with local constraints. At the impulsive instants, each agent can communicate with its neighboring agents over the network. Under certain conditions, the impulsive average quasi-consensus is achieved. It is shown that the state of average quasi-consensus is the optimal solution of the aforementioned unconstrained optimization problem, and the state of each agent can also reach the neighborhood of the optimal solution. Finally, two numerical examples show the effectiveness of the proposed impulsive average quasi-consensus algorithm. Moreover, the feasibility of the approach is verified by an application to one sensor network localization problem. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the stochastic synchronization problem of delayed multiagent networks with intermittent communications. Two kinds of impulsive effects are taken into account, ie, impulsive controller (positive impulsive effect) and impulsive disturbance (negative impulsive effect). Impulsive controller allows the synchronization to be realized and requires only state information exchange at discrete time instants such that the communication cost of bandwidth is reduced. Meanwhile, impulsive disturbance is inevitable in most of practical systems and therefore is taken into consideration at discrete time instants. Sufficient conditions for synchronization are given in terms of the graph topology, the control coupling gains, and the individual agent dynamics parameters, which indicates that synchronization can be realized if the impulsive effects coefficients and communication rate are suitably selected. Simulation results verify the effectiveness of the proposed synchronization protocol. [ABSTRACT FROM AUTHOR]

In this paper, some consensus problems are considered for time-delay multiagent networks with directed topologies. Since agents are driven by not only long-term but instant contact with their neighbors, dynamic behaviors of agents can be described by impulsive differential equations. A period of non time-delay and time-delay information and instantaneous information are adopted in the proposed algorithms. Moreover, robust problems with the corresponding ${H_{\infty }}$ performance are investigated for multiagent networks with external disturbances. Sufficient conditions are obtained such that consensus can be exponentially reached for multiagent networks with/without external disturbances. Numerical examples are given to demonstrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of distributed information estimation that is closely relevant to some network-based applications, such as distributed surveillance, cooperative localization, and optimization. We consider a problem where an application area containing multiple information sources of interest is divided into a series of subregions in which only one information source exists. The information is presented as a signal variable, which has finite states associated with certain probabilities. The probability distribution of information states of all the subregions constitutes a global information picture for the whole area. Agents with limited measurement and communication ranges are assumed to monitor the area, and cooperatively create a local estimate of the global information. To efficiently approximate the actual global information using individual agents’ own estimates, we propose an adaptive distributed information fusion strategy and use it to enhance the local Bayesian rule-based updating procedure. Specifically, this adaptive fusion strategy is induced by iteratively minimizing a Jensen–Shannon divergence-based objective function. A constrained optimization model is also presented to derive minimum Jensen–Shannon divergence weights at each agent for fusing local neighbors’ individual estimates. Theoretical analysis and numerical results are supplemented to show the convergence performance and effectiveness of the proposed solution. [ABSTRACT FROM PUBLISHER]

We propose a method to efficiently estimate the eigenvalues of any arbitrary (potentially weighted or directed) network of interacting dynamical agents in the presence of control inputs from dynamical observations. These observations are discrete, temporal measurements of the evolution of the aggregated outputs from a subset of agents (potentially one) during a finite time horizon. Notably, we do not require knowledge of which agents contribute to our measurements. We propose an efficient algorithm to exactly recover the (potentially complex) eigenvalues corresponding to network modes which are observable from the output measurements. The length of the sequence of measurements required by our method to generate a full reconstruction of the observable eigenvalue spectrum is at most three times the number of agents in the network, but in practice fewer are required, dependent on the number of observable network modes. The proposed technique can be applied to networks of non-autonomous multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations. [ABSTRACT FROM AUTHOR]

This paper surveys recent advances related to adaptation, learning, and optimization over networks. Various distributed strategies are discussed that enable a collection of networked agents to interact locally in response to streaming data and to continually learn and adapt to track drifts in the data and models. Under reasonable technical conditions on the data, the adaptive networks are shown to be mean square stable in the slow adaptation regime, and their mean square error performance and convergence rate are characterized in terms of the network topology and data statistical moments. Classical results for single-agent adaptation and learning are recovered as special cases. The performance results presented in this work are useful in comparing network topologies against each other, and in comparing adaptive networks against centralized or batch implementations. The presentation is complemented with various examples linking together results from various domains. [ABSTRACT FROM PUBLISHER]

In this paper, an optimal control design strategy for guaranteeing consensus achievement in a network of multiagent systems is developed. Minimization of a global cost function for the entire network guarantees a stable consensus with an optimal control effort. In solving the optimization problem, it is shown that the solution of the Riccati equation cannot guarantee consensus achievement. Therefore, a linearmatrix-inequality (LMI) formulation of the problem is used to address the optimization problem and to simultaneously resolve the consensus achievement constraint. Moreover, by invoking an LMI formulation, a semidecentralized controller structure that is based on the neighboring sets, i.e., the network underlying graph, can be imposed as an additional constraint. Consequently, the only information that each controller requires is the one that it receives from agents in its neighboring set. The global cost function formulation provides a deeper understanding and insight into the optimal system performance that would result from the global solution of the entire network of multiagent systems. Simulation results are presented to illustrate the capabilities and characteristics of our proposed multiagent team in achieving consensus. [ABSTRACT FROM AUTHOR]

Abstract: Robust globally stable model reference adaptive control (MRAC) laws recently derived for systems described by parabolic and hyperbolic partial differential equations (PDEs) with spatially-varying coefficients under distributed sensing and actuation are extended to heterogeneous multiagent networks characterized by parameter uncertainty. The extension is carried out using partial difference equations (PdEs) on graphs that preserve parabolic- and hyperbolic-like cumulative network behavior. Unlike in the PDE case, only boundary input is specified for the reference model. The algorithms proposed directly incorporate this boundary reference input into the reference PdE to generate the distributed admissible reference evolution profile followed by the agents. The agent evolution thus depends only on the interaction with the adjacent agents, making the system fully decentralized. Numerical examples are presented as well, including the case of the switched topology associated with a sudden loss of an agent. The resulting PdE MRAC laws inherit the robust linear structure of their PDE counterparts. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]