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We prove the existence of a multidimensional nontrivial invariant toroidal manifold for the Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds to the multicluster behavior of the oscillators phases. Contrary to the static coupling, the adaptive coupling strengths exhibit quasiperiodic oscillations preserving zero phase-difference within clusters. The derived sufficient conditions for the existence of the invariant manifold provide a tradeoff between the natural frequencies of the oscillators, coupling plasticity parameters, and the interconnection structure of the network. Furthermore, we study the robustness of the invariant manifold with respect to the perturbations of the interconnection topology, and establish structural, and quantitative constraints on the perturbation adjacency matrix preserving the invariant manifold. Additionally, we demonstrate the application of the new results to the problem of interconnection topology design, which consists in endowing the desired multicluster behavior to the network by controlling its interconnection structure. [ABSTRACT FROM AUTHOR]

This article studies how to estimate the weighted adjacency matrix of a network out of the state sequence of a model with binary-valued states, by using a recursive algorithm. In the considered system, agents display and exchange these binary-valued states generated from intrinsic quantizers. It is shown that stability of the model and identifiability of the system parameters can be guaranteed under continuous random noise. Under standard Gaussian noise, the problem of estimating the real-valued weighted adjacency matrix and the unknown quantization threshold is transformed to an optimization problem via a maximum likelihood approach. It is further verified that the unique solution of the optimization problem is the true parameter vector. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Numerical simulations are provided to illustrate developed results.

This article is concerned with distributed Nash equilibrium (NE) problem for multiplayer games under the Round-Robin (RR) protocol. For the purpose of effectively mitigating data congestion and saving communication resources, the RR protocol is adopted for each player, under which the player is permitted to transmit data to only one of its neighbors at each time instant. The resulting protocol-induced communication graph become time-varying and even disconnected, even though the original graph is assumed to be strongly connected. The aim of the addressed problem is to develop a distributed algorithm in the partial-decision information setting such the convergence of NE can be guaranteed under the $B$-strong connectivity of graphs and the row-stochasticity of weighted adjacency matrix. The sufficient condition on the convergence of the NE is derived for the algorithm with diminishing step-sizes. Some discussions are provided on convergence rate of the proposed algorithm. Finally, one numerical example is provided to verify the developed algorithm.

We provide necessary and sufficient conditions for the node systems, the graph adjacency matrix, and the input matrix such that a heterogeneous network of multi-input multi-output linear time-invariant (LTI) node systems with constant linear couplings is controllable or stabilizable through the external input. We also provide specializations of these general conditions for homogeneous networks. Finally, we give a very simple, necessary and sufficient condition under which a homogeneous network of single-input single-output LTI node systems is stable in the absence of the external input. [ABSTRACT FROM AUTHOR]

In this technical note, we consider the distributed surrounding of a convex target set by a group of agents with switching communication graphs. We propose a distributed controller to surround a given set with the same distance and desired projection angles specified by a complex-value adjacency matrix. Under mild connectivity assumptions, we give results in both consistent and inconsistent cases for the set surrounding in a plane. Also, we provide sufficient conditions for the multi-agent coordination when the convex set contains only the origin. [ABSTRACT FROM PUBLISHER]

This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks. [ABSTRACT FROM AUTHOR]

In this article, we study proximal type dynamics in the context of multiagent network games. We analyze several conjugations of this class of games, providing convergence results. Specifically, we look into synchronous/asynchronous dynamics with time-invariant communication network and synchronous dynamics with time-varying communication networks. Finally, we validate the theoretical results via numerical simulations on opinion dynamics. [ABSTRACT FROM AUTHOR]

We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions and show that the termination time in general only depends on the number of agents involved in the dynamics. To the best of our knowledge, that is the sharpest bound for the termination time of such dynamics that removes dependency of the termination time from the dimension of the ambient space, and connects the convergence speed of the dynamics to the eigenvalues of the adjacency matrix of the connectivity graph in the Hegselmann-Krause dynamics. This answers an open question in the paper by Bhattacharyya et al. on how to obtain a tighter upper bound for the termination time. Furthermore, we study the asynchronous Hegselmann-Krause model from a novel game-theoretic approach and show that the evolution of an asynchronous Hegselmann-Krause model is equivalent to a sequence of best response updates in a well-designed potential game. We then provide a polynomial upper bound for the expected time and expected number of switching topologies until the dynamic reaches an arbitrarily small neighborhood of its equilibrium points, provided that the agents update uniformly at random. This is a step toward analysis of heterogeneous Hegselmann-Krause dynamics. Finally, we consider the heterogeneous Hegselmann-Krause dynamics and provide a necessary condition for the finite termination time of such dynamics. In particular, we sketch some future directions toward more detailed analysis of the heterogeneous Hegselmann-Krause model. [ABSTRACT FROM AUTHOR]

In this note, the cooperative output regulation problem of heterogeneous linear multi-agent systems is investigated. Our approach is based on internal model and dynamic error feedback among the agents. Under some standard assumptions, the problem is solved by an internal model and a stabilizing H\infty controller. We showed that the exo-signal-free system is stabilized if each controlled agent is robust (in the sense of H\infty norm) to resist the disturbance measured by the second largest eigenvalue of the graph adjacency matrix. Then the synthesis problem is solved using algebraic Riccati equation. Furthermore, we showed that this condition is a generalization of existing results. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a distributed computing approach to solving large-scale robust stability problems on the simplex. Our approach is to formulate the robust stability problem as an optimization problem with polynomial variables and polynomial inequality constraints. We use Polya's theorem to convert the polynomial optimization problem to a set of highly structured linear matrix inequalities (LMIs). We then use a slight modification of a common interior-point primal-dual algorithm to solve the structured LMI constraints. This yields a set of extremely large yet structured computations. We then map the structure of the computations to a decentralized computing environment consisting of independent processing nodes with a structured adjacency matrix. The result is an algorithm which can solve the robust stability problem with the same per-core complexity as the deterministic stability problem with a conservatism which is only a function of the number of processors available. Numerical tests on cluster computers and supercomputers demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors and analyze systems with 100+ dimensional state-space. The proposed algorithms can be extended to perform stability analysis of nonlinear systems and robust controller synthesis. [ABSTRACT FROM AUTHOR]

A common pattern formation mechanism in multi-cellular organisms is lateral inhibition where the cells inhibit a particular function in their immediate neighbors through a contact signaling mechanism. We present a broad dynamical model that captures this mechanism and reveal the key properties that are necessary for patterning. The model consists of subsystems representing the biochemical reactions in individual cells, interconnected according to an undirected graph describing which cells are in contact. By using input-output properties of the subsystems and the spectral properties of the adjacency matrix for the contact graph, we provide verifiable conditions that determine when the spatially homogeneous steady-state loses its stability and what types of patterns emerge. We first study bipartite contact graphs and investigate the existence and stability of a “checkerboard” pattern that demonstrates the ability of neighboring cells to adopt distinct fates under lateral inhibition. Next, we exhibit a monotonicity property of the interconnected model for bipartite graphs and, under mild additional conditions, prove that almost every solution converges to one of the possible steady-states. Finally, we reveal a pattern that emerges in odd-length cycles, which are quintessential examples of non-bipartite graphs. A salient feature of this paper is that, unlike the existing literature, it does not restrict the number of cells and reactants. [ABSTRACT FROM AUTHOR]

A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept. [ABSTRACT FROM PUBLISHER]

The theory of structural controllability allows us to assess controllability of a network as a function of its interconnection graph and independently of the edge weights. Yet, existing structural controllability results require the weights to be selected arbitrarily and independently from one another and provide no guarantees when these conditions are not satisfied. In this note, we develop a new theory for structural controllability of networks with symmetric, thus constrained, weights. First, we show that network controllability remains a generic property even when the weights are symmetric. Then, we characterize necessary and sufficient graph-theoretic conditions for structural controllability of networks with symmetric weights: a symmetric network is structurally controllable if and only if it is structurally controllable without weight constraints. Finally, we use our results to assess structural controllability from one region of a class of empirically-reconstructed brain networks. [ABSTRACT FROM AUTHOR]

We consider transportation over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with initial and final marginal constraints on mass transport. We address the situation where initially the mass is concentrated on certain nodes and needs to be transported over a certain time period to another set of nodes, possibly disjoint from the first. The evolution is selected to be closest to a prior measure on paths in the relative entropy sense–such a construction is known as a Schrödinger bridge between the two given marginals. It may be viewed as an atypical stochastic control problem where the control consists in suitably modifying the prior transition mechanism. The prior can be chosen to incorporate constraints and costs for traversing specific edges of the graph, but it can also be selected to allocate equal probability to all paths of equal length connecting any two nodes (i.e., a uniform distribution on paths). This latter choice for prior transitions relies on the so-called Ruelle-Bowen random walker and gives rise to scheduling that tends to utilize all paths as uniformly as the topology allows. Thus, this Ruelle-Bowen law (\mathfrak M\mathrm {RB}) taken as prior, leads to a transportation plan that tends to lessen congestion and ensures a level of robustness. We also show that the distribution \mathfrak M\mathrm {RB} on paths, which attains the maximum entropy rate for the random walker given by the topological entropy, can itself be obtained as the time-homogeneous solution of a maximum entropy problem for measures on paths (also a Schrödinger bridge problem, albeit with prior that is not a probability measure). Finally we show that the paradigm of Schrödinger bridges as a mechanism for scheduling transport on networks can be adapted to graphs that are not strongly connected, as well as to weighted graphs. In the latter case, our approach may be used to design a transportation plan which effectively compromises between robustness and other criteria such as cost. Indeed, we explicitly provide a robust transportation plan which assigns maximum probability to minimum cost paths and therefore compares favorably with Optimal Mass Transportation strategies. [ABSTRACT FROM AUTHOR]

In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely the leaders. Our main result relates the controllability of such systems to the graph distances between the agents. More specifically, we present a graph topological lower bound on the rank of the controllability matrix. This lower bound is tight, and it is applicable to systems with arbitrary network topologies, coupling weights, and number of leaders. An algorithm for computing the lower bound is also provided. Furthermore, as a prominent application, we present how the proposed bound can be utilized to select a minimal set of leaders for achieving controllability, even when the coupling weights are unknown. [ABSTRACT FROM AUTHOR]

The consensus control of multiagent systems (MASs) over randomly switching communication topologies has drawn increasing attention from researchers, since the mean square consensus or the most surely consensus is significant and practical. This manuscript focuses on the output consensus problem for heterogeneous MASs with input saturation constraints over the Markovian randomly switching topologies. The main challenge of solving the concerned problem lies in the interplay among the heterogeneous dynamics, input saturation constraints and the Markovian randomly switching topologies. To overcome such a challenge, a class of distributed adaptive observers is first designed for all agents to deal with the uncertainty caused by the randomly switching topologies. Then, a class of local state observers is presented for estimating each agent’s state information. Based on the above steps, a class of antiwindup controllers is constructed and the control gain matrices are selected using only the dynamics information of each node. Finally, the effectiveness of the consensus protocol is demonstrated. [ABSTRACT FROM AUTHOR]

This article investigates the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems with switching topologies and infinite distributed communication delays. A novel distributed observer is proposed for each agent to estimate the state of the so-called exosystem by taking consideration of both switching topologies and infinite distributed communication delays. A distributed output feedback controller is then developed based on the internal model principle and the estimated state without using the prior knowledge of communication delays. It is shown via the newly developed Lyapunov-like method that the robust cooperative output regulation problem can be solved under some mild assumptions. Finally, a numerical example is given to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article develops a novel continuous-time algorithm based on the idea of adaptive strategy for solving a resource allocation optimization with nonsmooth objective functions and constraints over multiagent network. It is proved that the state solution is globally bounded and finally converges to an optimal solution to the nonsmooth convex resource allocation problem. Compared with the existing algorithms, the strong/strict convexity of the objective function is relaxed and only convexity is required. Moreover, by employing an exact penalty approach for the distributed optimization, the primal-dual variables is avoided to introduce. Therefore, the proposed algorithm has a simple structure with low dimensionality of state variables. To show the effectiveness and practicability of the presented algorithm, a numerical example and an application in power system are presented. [ABSTRACT FROM AUTHOR]

During the implementation of a cooperative algorithm, information about the agents’ velocity may be unavailable due to the space constraint and availability of sensors. Thus, it gives rise to the design of distributed average tracking (DAT) algorithms without using agents’ velocity measurements. These are denoted as velocity-free DAT problems. The existing literature has addressed such problems in the presence of an undirected graph for the reference signals with bounded position, velocity, and acceleration differences. We propose a velocity-free DAT algorithm under a weight-unbalanced strongly-connected digraph that represents the most general network structure for achieving DAT. Additionally, the proposed algorithm works for a broader range of time-varying references, having bounded acceleration differences among themselves. Linear stability theory is used to establish uniform ultimate boundedness of the errors for bounded acceleration differences. Asymptotic convergence of the errors is guaranteed for converging acceleration differences. Unlike the existing works, our DAT algorithm does not need any update law for the gains. Thus, the approach is computationally efficient. Numerical simulations with the comparison with the state-of-the-art demonstrate the performance of our algorithm over a wider range of time-varying references under weight-unbalanced graph. [ABSTRACT FROM AUTHOR]

In this article, the $\mathcal {H}_{\infty }$ optimization approach is used to study the consensusability margin optimization problems for distributed second-order sampled-data multiagent systems with communication uncertainties. The considered uncertainties are frequency-dependent and bounded in $\mathcal {H}_{\infty }$ norms. Specifically, for both the state-based protocols with relative damping and absolute damping, this article attempts to answer two questions: 1) how to characterize the control parameters for achieving robust consensus; and 2) what is the maximal consensusability margin and how to find, if one exists, the parameter to achieve this optimal performance. It is shown that the consensusability margin optimization problems are constraint optimization problems, which are to be specified by specific problem parameters and can be discussed by designing the network complementary sensitivity function matrices of the closed-loop multiagent systems. Moreover, it is shown that the infimums of the $\mathcal {H}_{\infty }$ norms of the network complementary sensitivity function matrices under both protocols are independent of network topologies. [ABSTRACT FROM AUTHOR]

This article aims at developing a scaling-function approach for distributed optimization of unbalanced multiagent networks under convex constraints. The distinguishing feature of the algorithm is that it does not employ agents’ out-degree information, nor does it require the estimation of the left eigenvector, corresponding to the zero eigenvalue, of the Laplacian matrix. Existing approaches for unbalanced networks either demand the knowledge on agents’ out-degrees, which is impractical in applications, where an agent might not be aware of the detection and employment of its information by other agents, or require every agent to be equipped with a network-sized estimator, causing an additional $n^2$ storage and communication cost with $n$ being the network size. The results exhibit an inherent connection between the selection of the scaling factor and the convergence property of the algorithm, among other known factors such as the network topology and the boundedness of the subgradients of the local objective functions. Numerical examples are provided to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

The design of distributed Nash equilibrium-seeking strategies for games in which the involved players are of second-order integrator-type dynamics is investigated in this article. Noticing that velocity signals are usually noisy or not available for feedback control in practical engineering systems, this article supposes that the velocity signals are not accessible for the players. To deal with the absence of velocity measurements, two estimators are designed. The first estimator is established by employing an observer, which has the same order as the players’ dynamics, to estimate the unavailable system states (e.g., the players’ velocities). The second estimator is designed based on a high-pass filter and is motivated by the incentive to reduce the order of the estimator, which in turn saves the computation costs of the seeking algorithms. On the basis of the designed observers/filters, distributed Nash equilibrium-seeking strategies are then established through incorporating them with consensus and gradient algorithms. It is analytically proven that the players’ actions can be regulated to the Nash equilibrium point and their velocities can be regulated to zero by utilizing the proposed velocity-free Nash equilibrium-seeking strategies. A numerical example is provided for the verification of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article develops a distributed solution to the fully heterogeneous containment control problem (CCP), for which not only the followers’ dynamics but also the leaders’ dynamics are nonidentical. A novel formulation of the fully heterogeneous CCP is first presented in which each follower constructs its virtual exosystem. To build these virtual exosystems by followers, a novel distributed algorithm is developed to calculate the so-called normalized level of influences (NLIs) of all leaders on each follower, and a novel adaptive distributed observer is designed to estimate the dynamics and states of all leaders that have an influence on each follower. Then, a distributed control protocol is proposed based on the cooperative output regulation framework, utilizing this virtual exosystem. Based on the estimations of leaders’ dynamics and states and NLIs of leaders on each follower, the solutions of the so-called linear regulator equations are calculated in a distributed manner, and consequently, a distributed control protocol is designed for solving the output containment problem. Finally, theoretical results are verified by performing numerical simulations. [ABSTRACT FROM AUTHOR]

Group consensus implies reaching multiple groups where agents belonging to the same cluster reach state consensus. This article focuses on linear multiagent 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 underlying graph in the literature. Under a designed controller gain, lower bound of the overall coupling strength for achieving group consensus is specified. Moreover, the pattern of the multiple consensus states formed by all clusters is characterized when the overall coupling strength is large enough. [ABSTRACT FROM AUTHOR]

In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. The main approach relies on the unique decomposition of the inverse of power spectral density matrix (IPSDM) obtained from observed nodes as a sum of sparse and low-rank matrices. We provide conditions and methods for decomposing the IPSDM into sparse and low-rank components. The sparse component yields moral graph (MG) associated with the observed nodes, and the low-rank component retrieves parents, children and spouses (the Markov Blanket) of the hidden nodes. The article provides necessary and sufficient conditions for the unique decomposition of a given skew symmetric matrix into sum of a sparse skew symmetric and a low-rank skew symmetric matrices. For a large class of systems, the unique decomposition of imaginary part of the IPSDM of observed nodes, a skew symmetric matrix, into the sparse and the low-rank components is sufficient to identify the MG of the observed nodes as well as the Markov Blanket of latent nodes. For a large class of systems, all spurious links in the MG formed by the observed nodes can be identified. Assuming conditions on hidden nodes required for identifiability, links between hidden and observed nodes can be reconstructed, thus retrieving the exact topology of the network from the IPSDM. Moreover, for finite data, we provide bounds on entry-wise distance between the true and the estimated IPSDMs. [ABSTRACT FROM AUTHOR]

In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective resistances in some prototypical directed graphs. This exploration highlights cases where our notion of effective resistance for directed graphs behaves analogously to our experience from undirected graphs, as well as cases where it behaves in unexpected ways. [ABSTRACT FROM PUBLISHER]

This article studies the tracking control problem of networked multiagent systems under both multiple networks and event-triggered mechanisms. Multiple networks are to connect multiple agents and reference systems with decentralized controllers to guarantee their information transmission, whereas the event-triggered mechanisms are to reduce the information transmission via the networks. In this article, each agent has a network to communicate with its controller and reference system, and all networks are independent and asynchronous and have local event-triggered mechanisms, which are based on local measurements and determine whether the local measurements need to be transmitted via the corresponding network. To address this scenario, we first implement the emulation-based approach to develop a novel hybrid model for the tracking control of networked multiagent systems. Next, sufficient conditions are derived and decentralized event-triggered mechanisms are designed to guarantee the desired tracking performance. Furthermore, the proposed approach is applied to derive novel results for the event-triggered observer design problem of networked multiagent systems. Finally, two numerical examples are presented to illustrate the validity of the developed results. [ABSTRACT FROM AUTHOR]

In this article, we consider distributed stochastic optimization over randomly switching networks, where agents collaboratively minimize the average of all agents’ local expectation-valued convex cost functions. Due to the stochasticity in gradient observations, distributedness of local functions, and randomness of communication topologies, distributed algorithms with an exact convergence guarantee under fixed step-sizes have not been achieved yet. This work incorporates variance reduction scheme into the distributed stochastic gradient tracking algorithm, where local gradients are estimated by averaging across a variable number of sampled gradients. With an identically and independently distributed random network, we show that all agents’ iterates converge almost surely to the same optimal solution under fixed step-sizes. When the global cost function is strongly convex and the sample size increases at a geometric rate, we prove that the iterates geometrically converge to the unique optimal solution, and establish the iteration, oracle, and communication complexity. The algorithm performance, including rate and complexity analysis, are further investigated with constant step-sizes and a polynomially increasing sample size. Finally, the empirical algorithm performance are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme. [ABSTRACT FROM AUTHOR]

This article addresses distributed estimation problems over asynchronous networks in a set membership framework. The agents in the network asynchronously collect and process measurements, communicate over a possibly time-varying and unbalanced directed graph and may have nonnegligible computation times. Measurements are affected by bounded errors so that they define feasible sets containing the unknown parameters to be estimated. The proposed algorithm requires each agent to compute a weighted average of its estimate and those of its neighbors and to project it onto a local feasible set. By assuming convexity of the measurement sets, the local estimates are shown to converge to a common point belonging to the global feasible set. [ABSTRACT FROM AUTHOR]

In this article, we consider a collective decision-making process in a network of agents described by a nonlinear interconnected dynamical model with sigmoidal nonlinearities and signed interaction graph. The decisions are encoded in the equilibria of the system. The aim is to investigate this multiagent system when the signed graph representing the community is not structurally balanced and in particular as we vary its frustration, i.e., its distance to structural balance. The model exhibits bifurcations, and a “social effort” parameter, added to the model to represent the strength of the interactions between the agents, plays the role of bifurcation parameter in our analysis. We show that, as the social effort increases, the decision-making dynamics exhibit a pitchfork bifurcation behavior where, from a deadlock situation of “no decision” (i.e., the origin is the only globally stable equilibrium point), two possible (alternative) decision states for the community are achieved (corresponding to two nonzero locally stable equilibria). The value of social effort for which the bifurcation is crossed (and a decision is reached) increases with the frustration of the signed network. [ABSTRACT FROM AUTHOR]

This technical article addresses the formation stabilization problem for multiagent systems (MASs) composed of dynamical agents moving within an obstacle-cluttered environment and sharing information via nonideal wireless communication networks. A novel distributed cooperative navigation function based control strategy is proposed, which drives the MAS to a desired formation without any collision while counteracting the presence of unavoidable communication impairments originated by the wireless network. By recasting the formation stabilization problem into a consensus one and by combining the Lyapunov stability theory with Halanay’s lemma, uniformly ultimately bounded stability of the whole delayed closed-loop system is proved. In the special case of an obstacle-free environment, our approach guarantees exponential stability of the closed-loop networked system. The stability analysis also provides an estimation of the delay upper bound and allows to evaluate the stability margins with respect to the latencies that can be observed in practical application scenarios. Theoretical derivations are verified through nontrivial simulations. [ABSTRACT FROM AUTHOR]

A biased assimilation model of opinion dynamics is a nonlinear model, in which opinions exchanged in a social network are multiplied by a state-dependent term having the bias as exponent and expressing the bias of the agents toward their own opinions. The aim of this article is to extend the bias assimilation model to signed social networks. We show that while for structurally balanced networks, polarization to an extreme value of the opinion domain (the unit hypercube) always occurs regardless of the value of the bias, for structurally unbalanced networks, a stable state of indecision (corresponding to the centroid of the opinion domain) also appears, at least for small values of the bias. When the bias grows and passes a critical threshold, which depends on the amount of “disorder” encoded in the signed graph, then a bifurcation occurs and opinions become again polarized. [ABSTRACT FROM AUTHOR]

Sensor resolution, which is one of the most important parameters/specifications for almost all kinds of sensors, plays an important role in any signal processing problems. This article deals with the distributed filtering problem for a class of discrete time-varying stochastic systems subject to nonlogarithmic sensor resolution and stochastic nonlinearities. The soft measurement technique is exploited in the filter design to overcome the difficulties resulting from the sensor-resolution-induced (SRI) uncertainty. The aim of the presented filtering problem is to construct the distributed filter over a sensor network such that in the presence of SRI uncertainty and stochastic nonlinearity, an upper bound on the filtering error covariance is guaranteed and subsequently minimized by appropriately designing the filer parameters at each time instant. Moreover, a matrix simplification method is utilized to tackle the difficulties stemming from the sparsity of sensor networks. Finally, a numerical example is employed to illustrate the effectiveness of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

In this article, a noncooperative game in which the engaged players are of double integrator-type dynamics, is investigated. The dynamics of the players are considered to be subject to unknown time-varying disturbances and unmodeled terms. Besides, the communication topology among the players suffers from attacks and time-varying communication delays. To find a Nash equilibrium for such games, a distributed robust Nash equilibrium seeking algorithm is proposed. By utilizing average dwell-time and time-ratio constraints to tackle the attacks, the closed-loop system is modeled as a hybrid system with memory. To analyze the stability of the distributed switched algorithm, a Lyapunov functional is constructed, by which we show the uniform global asymptotic stability of the equilibrium. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

This article is concerned with the global leader-following consensus problem of the input-constrained double-integrator multiagent systems. By utilizing a Lyapunov-like function consisting of a positive semidefinite term and an integral term, a class of bounded static linear protocols are proposed to ensure that the global leader-following consensus problem for homogeneous multiagent systems is solved in a fully distributed manner for all undirected communication graphs. As a further result, the global consensus problem for heterogeneous multiagent systems under directed communication graphs is also considered and two different distributed observer-based bounded linear protocols are proposed to solve such a problem also in a fully distributed manner. The most significant advantages of this article are that the system under consideration is more general, the designed protocols are linear, and the global consensus in a fully distributed manner can be guaranteed. A numerical example shows the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The discrete distributed observer is developed recently to solve the cooperative output regulation problem. The validation of the existing discrete distributed observer depends on the establishment of the communication network. In some practical applications, only the sensor network can be established among all agents. To handle such cases, we propose a sensory feedback-based discrete distributed observer, which depends on the relative output of neighboring agents. In contrast to existing results, the design of the discrete distributed observer and cooperative output regulation analysis should be conducted simultaneously. Resorting to the small-gain theorem, we develop a small-gain condition-based approach and a low-gain-based approach, respectively. By these two approaches, we demonstrate that the discrete distributed observer holds and the cooperative output regulation problem of heterogeneous discrete-time linear multiagent systems can be solved. [ABSTRACT FROM AUTHOR]

In this article, we propose a distributed negotiation framework that allows a set of cooperative agents to find a common ground with their neighbors while attempting to modify their initial opinion by the least possible amount. Based on such a framework, we develop a distributed agreement approach where the effort spent in the local agreement reflects the relevance of the agents in a weighted consensus process. In particular, we assume that players whose ideas happen to satisfactory mediate the standpoint of their interlocutors will end-up being more influential in the overall decision-making process. We conclude the article by applying the proposed methodology in the context of distributed data aggregation scenarios, as a way to mitigate the effect of outliers (e.g., faulty sensors). [ABSTRACT FROM AUTHOR]

A directed acyclic graph (DAG) is a common topology in biological, engineering, and social networks. A network topology is critical in determining a collective behavior of a network dynamic system. For example, the convergence rate of a consensus behavior in a multiagent system relies on the eigenvalues of the Laplacian associated with the network topology. This article aims to analyze the influence of adding a reverse edge into a DAG on convergence rate. It reveals the existence of the so-called interfering reverse edges; adding one single edge in this category can reduce the so-called dominant convergence rate even for a large network. More specifically, a necessary and sufficient condition of an interfering reverse edge is explicitly constructed. According to the condition, a computationally efficient method is proposed to assess an interfering reverse edge. [ABSTRACT FROM AUTHOR]

In this article, we present a novel methodology to address the optimal output consensus problem for multiagent systems. We propose a distributed variable transformation that recasts the aforementioned problem into a simpler regulation problem of the new variables. The transformation requires only relative output measurements and is independent of any underlying agent dynamics and therefore applicable to a general class of systems. Classical control techniques, which take into account the agent dynamics and only need the relative outputs to be shared between neighbors, can then be employed to regulate the new variables. We utilize the methodology to address, for the first time, the problem of optimal output consensus for unknown pure-feedback agents with disturbances and state delays. Simulation studies on a group of continuous stirred tank reactors illustrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article investigates the second-order consensus issue for multiagent systems subject to both limited communication resources and replay attacks. First, an asynchronous dynamic edge event-triggered (DEET) communication scheme is developed to reduce the utilization of network resources in the absence of attacks. Then, we further consider the case of replay attacks launched by multiple adversaries, under which the transmitted information is maliciously replaced by a previous unnecessary message. To overcome the impact caused by replay attacks, a modified DEET scheme and an effective attack-resilient consensus protocol are well constructed, both of which successfully guarantee second-order consensus in the presence of replay attacks. In addition, internal dynamic variables are utilized in the proposed DEET schemes such that the triggering time sequence does not exhibit Zeno behavior. Finally, one numerical example is provided to illustrate our theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we investigate the interval consensus for a network of agents with flocking dynamics, i.e., second-order multiagent systems, where each agent imposes an interval constraint on its preferred consensus values, with the aim of driving the agent into a favorable interval. Specifically, we work on two different frameworks of interval constraints, viz., the first one that the node states are constrained in their own constraint intervals and the second one that the node states are constrained in their neighbors’ constraint intervals. For both of the frameworks, we provide a complete solution to the equilibrium seeking problem by resolving a system of nonlinear equations. It is proved that if the underlying graph is strongly connected and the intersection of constraint intervals is empty, then there exists a unique equilibrium point; and if the intersection is nonempty, then there exist multiple equilibrium points, all of which lead to state consensus. We also establish several conditions for the local stability of the unique equilibrium point (corresponding to the case with empty intersection of constraint intervals) or local constraint consensus (corresponding to the case with nonempty intersection of constraint intervals) by invoking Lyapunov’s indirect method. Characterization of the global behavior of such a second-order multiagent system is technically rather challenging at this stage. As a first step toward this end, we show in two special cases that global convergence to the unique equilibrium point or state consensus can be guaranteed by employing Lyapunov stability theory and robust analysis techniques. Finally, some numerical examples are provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel. [ABSTRACT FROM AUTHOR]