Rebels Lead to the Doctrine of the Mean: A Heterogeneous DeGroot Model

The DeGroot model is one of the most classical models in the field of opinion dynamics. The standard DeGroot model assumes that agents are homogeneous and update their opinions in the direction of a weighted average of their neighbors’ opinions. One natural question is whether a second type of agents could significantly change the main properties of the model. The authors address this question by introducing rebels, who update their opinions toward the opposite of their neighbors’ weighted average. The authors find that the existence of rebels remarkably affects the opinion dynamics. Under certain mild conditions, the existence of a few rebels will lead the group opinion to the golden mean, regardless of the initial opinions of the agents and the structure of the learning network. This result is completely different from that of the standard DeGroot model, where the final consensus opinion is determined by both the initial opinions and the learning topology. The study then provides new insights into understanding how heterogeneous individuals in a group reach consensus and why the golden mean is so common in human society.     

Consensus of Flocks under M-Nearest-Neighbor Rules

This paper investigates a class of flocks with an M-nearest-neighbor rule,where each agent’s neighbors are determined according to M nearest agents with M being a given integer,rather than all the agents within a fixed metric distance as in the well-known Vicsek’s model.Such a neighbor rule has been validated by biologists through experiments and the authors will prove that,similar to the Vicsek’s model,such a new neighbor rule can also achieve consensus under some conditions imposed only on the system’s speed and the number M,n,without resorting to any priori connectivity assumptions on the trajectory of the system.In particular,the authors will prove that if the number M is proportional to the population size n,then for any speed v,the system will achieve consensus with large probability if the population size is large enough.     

Distributed Algorithm for Robust Resource Allocation with Polyhedral Uncertain Allocation Parameters

This paper studies a distributed robust resource allocation problem with nonsmooth objective functions under polyhedral uncertain allocation parameters. In the considered distributed robust resource allocation problem, the (nonsmooth) objective function is a sum of local convex objective functions assigned to agents in a multi-agent network. Each agent has a private feasible set and decides a local variable, and all the local variables are coupled with a global affine inequality constraint, which is subject to polyhedral uncertain parameters. With the duality theory of convex optimization, the authors derive a robust counterpart of the robust resource allocation problem. Based on the robust counterpart, the authors propose a novel distributed continuous-time algorithm, in which each agent only knows its local objective function, local uncertainty parameter, local constraint set, and its neighbors’ information. Using the stability theory of differential inclusions, the authors show that the algorithm is able to find the optimal solution under some mild conditions. Finally, the authors give an example to illustrate the efficacy of the proposed algorithm.     

Consensus control design for multi-agent systems using relative output feedback

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.     

Group consensus for multiple networked Euler-Lagrange systems with parametric uncertainties

In this paper,a group consensus problem is investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters.In the group consensus problem,the agents asymptotically reach several different states rather than one consistent state.A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem.It is shown that the group consensus is reachable even when the system contains the uncertain parameters.Furthermore,the multi-group consensus is discussed as an extension of the couple-group consensus,and then the group consensus with switching topology is considered.Simulation results are finally provided to validate the effectiveness of the theoretical analysis.     

Mean Square Average Generalized Consensus of Multi-Agent Systems Under Time-Delays and Stochastic Disturbances

Compared with the traditional consensus problem, this paper deals with the mean square average generalized consensus(MSAGC) of multi-agent systems under fixed directed topology, where all agents are affected by stochastic disturbances. Distributed protocol depending on delayed time information from neighbors is designed. Based on Lyapunov stability theory, together with results from matrix theory and It o s derivation theory, the linear matrix inequalities approach is used to establish sufficient conditions to ensure MSAGC of multi-agent systems. Finally, numerical simulations are provided to illustrate the theoretical results.     

Coordination Control for a Class of Multi-Agent Systems Under Asynchronous Switching

This paper studies the coordination control of nonlinear multi-agent systems under asynchronous switching, including consensus, tracking control, and containment. The asynchronous switching considered here means that the switching of the controller lags behind the mode's switching for each agent. So the matched controller is interrupted by the delayed switching. For the situation, the authors give some new results by applying the conventional distributed control protocol. The authors show that all agents can achieve consensus. Secondly, the authors show that all followers can track the actual leader. Thirdly, the authors show that all followers will converge to the convex hull spanned by the dynamic leaders as time goes on. Numerical simulations are also provided and the results show highly consistent with the theoretical results.     

Bipartite Consensus of Discrete-Time Double-Integrator Multi-Agent Systems with Measurement Noise

The effects of measurement noise are investigated in the context of bipartite consensus of multi-agent systems. In the system setting, discrete-time double-integrator dynamics are assumed for the agent, and measurement noise is present for the agent receiving the state information from its neighbors. Time-varying stochastic bipartite consensus protocols are designed in order to lessen the harmful effects of the noise. Consequently, the state transition matrix of the closed-loop system is analyzed, and sufficient and necessary conditions for the proposed protocol to be a mean square bipartite consensus protocol are given with the help of linear transformation and algebraic graph theory. It is proven that the signed digraph to be structurally balanced and having a spanning tree are the weakest communication assumptions for ensuring bipartite consensus. In particular, the proposed protocol is a mean square bipartite average consensus one if the signed digraph is also weight balanced.     

Soft-control for collective opinion of weighted DeGroot model

The DeGroot model is a classic model to study consensus of opinion in a group of individuals(agents). Consensus can be achieved under some circumstances. But when the group reach consensus with a convergent opinion value which is not what we expect, how can we intervene the system and change the convergent value? In this paper a mechanism named soft control is first introduced in opinion dynamics to guide the group's opinion when the population are given and evolution rules are not allowed to change. According to the idea of soft control, one or several special agents,called shills, are added and connected to one or several normal agents in the original group. Shills act and are treated as normal agents. The authors prove that the change of convergent opinion value is decided by the initial opinion and influential value of the shill, as well as how the shill connects to normal agents. An interesting and counterintuitive phenomenon is discovered: Adding a shill with an initial opinion value which is smaller(or larger) than the original convergent opinion value dose not necessarily decrease(or increase) the convergent opinion value under some conditions. These conditions are given through mathematical analysis and they are verified by the numerical tests. The authors also find out that the convergence speed of the system varies when a shill is connected to different normal agents. Our simulations show that it is positively related to the degree of the connected normal agent in scale-free networks.     

Model Reference Adaptive Control for Networked Distributed Systems with Strong Interconnections and Communication Delays

In recent years, networked distributed control systems (NDCS) have received research attention. Two of the main challenges that such systems face are possible delays in the communication network and the effect of strong interconnections between agents. This paper considers an NDCS that has delays in the communication network, as well as strong interconnections between its agents. The control objective is to make each agent track efficiently a reference model by attenuating the effect of strong interconnections via feedback based on the delayed information. First, the authors assume that each agent knows its own dynamics, as well as the interconnection parameters, but receives information about the states of its neighbors with some communication delay. The authors propose a distributed control scheme and prove that if the interconnections can be weakened and if the communication delays are small enough, then the proposed scheme guarantees that the tracking error of each agent is bounded with a bound that depends on the size of the weakened interconnections and delays, and reduces to zero as these uncertainties reduce to zero. The authors then consider a more realistic situation where the interconnections between agents are unknown despite the cooperation and sharing of state information. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense with respect to the size of the weakened interconnections and delays, provided the weakened interconnections and time delays are small enough. The authors then consider the case that each agent knows neither its dynamics nor the interconnection matrices. For this case the authors propose a distributed adaptive control scheme and prove that the proposed scheme guarantees that the tracking errors are bounded and small in the mean square sense provided the weakened interconnections and time delays are small enough. Finally, the authors present an illustrative example to present the applicability and effectiveness of the proposed schemes.     

Distributed tracking control of second-order multi-agent systems under measurement noises

This paper considers a leader-following tracking control problem for second-order multiagent systems（MASs） under measurement noises and directed communication channels.It is assumed that each follower-agent can measure the relative positions and velocities of its neighbors in a noisy environment.Based on a novel velocity decomposition technique,a neighbor-based control law is designed to realize local control strategies for these continuous-time agents.It is shown that the proposed consensus protocol can guarantee that all the follower-agents track the active leader.In addition,this result is extended to a more general case with switching topologies.Finally,a numerical example is given for illustration.     

Finite Time Consensus Problem for Multiple Non-Holonomic Agents with Communication Delay

In this paper, finite time consensus problem is discussed for multiple non-holonomic mobile agents with constant communication delay. The objective is to design non-smooth distributed control laws such that multiple non-holonomic mobile agents can be all in agreement within any given finite time larger than communication delay. The authors propose a novel switching control strategy with the help of Lyapunov-based method and graph theory.     

Biased Learning Creates Overconfidence

The aim of this paper is to develop a multi-period economic model to interpret how the people become overconfident by a biased learning that people tend to attribute the success to their abilities and failures to other factors. The authors suppose that the informed trader does not know the distribution of the precision of his private signal and updates his belief on the distribution of the precision of his knowledge by Bayer’s rule. The informed trader can eventually recognize the value of the precision of his knowledge after an enough long time biased learning, but the value is overestimated which leads him to be overconfident. Furthermore, based on the definition on the luckier trader who succeeds the same times but has the larger variance of the knowledge, the authors find that the luckier the informed trader is, the more overconfident he will be; the smaller the biased learning factor is, the more overconfident the informed trader is. The authors also obtain a linear equilibrium which can explain some anomalies in financial markets, such as the high observed trading volume and excess volatility.     

Information revelation in sequential auctions with uncertainties about future objects

In many auctions, buyers know beforehand little about objects to be sold in the future. Whether and how to reveal information about future objects is an important decision problem for sellers. In this paper, two objects are sold sequentially and each buyer’s valuation for the second object is k times that for the first one, and the true value of k is sellers’ private information. The authors identify three factors which affect sellers’ revelation strategies: The market’s competition intensity which is characterized by the number of buyers, buyers’ prior information about the second object, and the difference degree between two objects which is characterized by k. The authors give not only conditions under which revealing information about the second object in advance benefits the seller, but also the optimal releasing amount of information in the market with two sellers and one seller, respectively.     

Distributed High-Gain Attitude Synchronization Using Rotation Vectors

This paper addresses attitude synchronization problems for systems of multiple rigid-body agents with directed interconnection topologies.Two scenarios which differ in available information are considered.In the first scenario the agents can obtain their rotations and angular velocities relative to an inertial reference frame and transmit these information to their neighbors,while in the second scenario the agents can only obtain their own angular velocities and measure the relative rotations and relative angular velocities of their neighbors.By using rotation vectors and the high gain control,the authors provide torque control laws asymptotically synchronizing the rotations of the system almost globally for the first scenario and with initial rotations of the agents contained in a convex ball of SO(3)for the second scenario.An illustrative example is provided to show the synchronization results for both scenarios.     

Differentially Private Distributed Parameter Estimation

Data privacy is an important issue in control systems, especially when datasets contain sensitive information about individuals. In this paper, the authors are concerned with the differentially private distributed parameter estimation problem, that is, we estimate an unknown parameter while protecting the sensitive information of each agent. First, the authors propose a distributed stochastic approximation estimation algorithm in the form of the differentially private consensus+innovations(DP-CI...     

Hidden Markov Models: Inverse Filtering,Belief Estimation and Privacy Protection

A hidden Markov model(HMM) comprises a state with Markovian dynamics that can only be observed via noisy sensors. This paper considers three problems connected to HMMs, namely,inverse filtering, belief estimation from actions, and privacy enforcement in such a context. First, the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter. Next, the authors consider a rational decision-maker that forms a private belief(posterior distribution) on the state of the world by filtering private information. The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent. In the setting of adversarial systems, the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions. Applications range from financial portfolio investments to life science decision systems.     

Consensus of Linear Multi-Agent Systems with Persistent Disturbances via Distributed Output Feedback

This paper addresses the consensus problem of general linear multi-agent systems with persistent disturbances by distributed output feedback. Suppose that states of agents can not be obtained directly. Several estimators are designed to observe states of agents and the unknown disturbances.A protocol is proposed to drive all agents achieve consensus. Based on the method of model transformation and the property of permutation matrix, sufficient conditions for consensus are obtained in terms of linear matrix inequalities. Finally, simulations are given to show the effectiveness of presented results.     

群体研讨中的共识分析和评价技术

实时、准确地对共识状态做出分析和评价是在综合集成研讨厅中组织好群体研讨的重要前提。为此,提出了一种称之为CAI的群体研讨中的共识分析和评价技术。依据CAI开发的软件能够根据发言之间的语义关系和研讨人的权重自动识别出共识状态,而用户可以依据CAI识别的结果干预研讨进程以便提高研讨的效率和有效性;同时,CAI软件还能够在用户的指导下学习从而增强其适应性。讨论了CAI的应用环境、分析模型、实现方法,并说明了CAI软件的工作过程和性能测试结果。     

Event-Triggered Consensus for Discrete-Time Multi-agent Systems with Parameter Uncertainties Based on a Predictive Control Scheme

In this paper, the event-triggered consensus for linear discrete-time multi-agent systems with parameter uncertainties is investigated. The parameter uncertainty is assumed to be normbounded. An event-triggered consensus protocol based on the predictive control method is proposed to make the multi-agent system achieve consensus. And for the design of the consensus protocol, the problem of estimating the control input is transformed into the problem of estimating state differences between agents. Furthermore, the event-triggered consensus protocol proposed in this paper only demands each agent to mornitor its state to determine its event-triggered instants. A sufficient existence condition for the consensus protocol is proposed based on the linear matrix inequality. And a sufficient condition for the nonexistence of the Zeno-like behaviour is also derived. Finally, a numerical example is given to illustrate that the event-triggered consensus protocol proposed in this paper can make the multi-agent system with parameter uncertainties achieve consensus effectively.