Group Decision Value Research Articles

Privacy-Preserving Consensus for Multi-Agent Systems via Node Decomposition Strategy

This paper proposes two kinds of algorithms to achieve privacy-preserving consensus of multi-agent systems over undirected graphs via node decomposition mechanism and homomorphic cryptography technique. Based on the number of neighboring nodes ( |\mathscr N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> |), every agent is decomposed into |\mathscr N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> | subagents, which are connected as a chain graph. Note that every subagent connects one and only one non-homologous subagent (generated by different agents). Information interaction between non-homologous subagents is encrypted by a homomorphic cryptography algorithm, and homologous subagents exchange information directly. In this regard, the proposed node decomposition mechanism enhances the privacy of the initial values without increasing the computational complexity of encryption. The first privacy-preserving algorithm can achieve the accurate average consensus, which means that the agreement value of every subagent is consistent with the original average consensus value. The second algorithm studies the privacy-preserving scaled consensus problem without a priori knowledge about the underlying graph. Although the final convergence values of subagents do not keep exactly the same, homologous subagents can compute the original group decision value by resorting to the product of the limit value and agent's degree. Importantly, this algorithm also guarantees the privacy of group decision value of the whole system. Besides, it is proved that the privacy of the initial value can be preserved if the agent has at least one neutral neighbor.

Dynamic Event-triggered Consensus Control of Discrete-time Linear Multi-agent Systems

Abstract We consider the distributed event-triggered consensus control problem of linear multi-agent systems in the discrete-time domain. The agents interact locally and exchange their state information with each other to reach a group decision value. We develop event-triggering protocols to facilitate opportunistic inter-agent communication and control updates for saving energy expenses. Continuous communication is avoided in triggering the conditions for monitoring and controller updates. Our general approach is to employ event-triggering laws with threshold mechanisms that depend on the states of the agents. We start with a static version and then generalize it so that it entails an internal auxiliary variable to regulate the threshold dynamically for each agent. Lyapunov-based design methods dictate when agents should communicate and update their control so that the network achieves consensus. A numerical example is provided to illustrate the efficacy of theoretical analysis.

Prescribed-Time Consensus and Containment Control of Networked Multiagent Systems.

In this paper, we present a new prescribed-time distributed control method for consensus and containment of networked multiple systems. Different from both regular finite-time control (where the finite settling time is not uniform in initial conditions) and the fixed-time control (where the settling time cannot be preassigned arbitrarily), the proposed one is built upon a novel scaling function, resulting in prespecifiable convergence time (the settling time can be preassigned as needed within any physically allowable range). Furthermore, the developed control scheme not only ensures that all the agents reach the average consensus in prescribed finite time under undirected connected topology, but also ensures that all the agents reach a prescribed-time consensus with the root's state being the group decision value under the directed topology containing a spanning tree with the root as the leader. In addition, we extend the result to prescribed-time containment control involving multiple leaders under directed communication topology. Numerical examples are provided to verify the effectiveness and the superiority of the proposed control.

Reach a nonlinear consensus for MAS via doubly stochastic quadratic operators

ABSTRACTThis technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators (DSQOs) for coordination of consensus problem in multi-agent systems (MAS). We derive the conditions for ensuring that every agent reaches consensus on a desired rate of the group's decision where the group decision value in its agent's initial statuses varies. Besides that, we investigate a nonlinear protocol sub-class of extreme DSQO (EDSQO) to reach a consensus for MAS to a common value with nonlinear low-complexity rules and fast time convergence if the interactions for each agent are not selfish. In addition, to extend the results to reach a consensus and to avoid the selfish case we specify a general class of DSQO for reaching a consensus under any given case of initial states. The case that MAS reach a consensus by DSQO is if each member of the agent group has positive interactions of DSQO (PDSQO) with the others. The convergence of both EDSQO and PDSQO classes is found to be directed towards the centre point. Finally, experimental simulations are given to support the analysis from theoretical aspect.

Solving a modified consensus problem of linear multi-agent systems

A distributed protocol is proposed for a modified consensus problem of a network of agents that have the same continuous-time linear dynamics. Each agent estimates its own state using its output information and then sends the estimated state to its neighbor agents for the purpose of reaching a consensus. The modified consensus problem requires the group decision value to be a linear function of initial states and initial estimated states of all agents in the network, and the transformation matrix associated with this linear function not to be a zero matrix. It is proved that under the proposed control protocol, the modified consensus problem can be solved if and only if the system matrices of the agent’s dynamics are stabilizable and detectable, the input matrix is not a zero matrix, and the communication topology graph has a spanning tree. The proposed protocol can also be extended to multi-agent systems where agents are described by discrete-time linear dynamics. The corresponding necessary and sufficient conditions are provided as well.

Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction

Nonlinear consensus protocols for dynamic directed networks of multi-agent systems with fixed and switching topologies are investigated separately in this paper. Based on the centre manifold reduction technique, nonlinear consensus protocols are presented. We prove that a group of agents can reach a β-consensus, the value of which is the group decision value varying from the minimum and the maximum values of the initial states of the agents. Moreover, we derive the conditions to guarantee that all the agents reach a β–consensus on a desired group decision value. Finally, a simulation study concerning the vertical alignment manoeuvere of a team of unmanned air vehicles is performed. Simulation results show that the nonlinear consensus protocols proposed are more effective than the linear protocols for the formation control of the agents and they are an improvement over existing protocols.

Algebraic criteria for consensus problems of continuous-time networked systems

This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.

Algebraic Criteria for Consensus Problems of Discrete-Time Networked Systems

This paper is mainly devoted to the algebraic criteria for consensus problems of discrete-time networked systems with the fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first correlated with the connectivity of a digraph, and then the relations between a class of Laplacian-type matrix and the stochastic matrix are established. Based on these tools, some necessary and/or sufficient algebraic conditions are proposed, which can directly determine whether the consensus problem can be solved or not. Furthermore, it is proved that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behavior of the system. Particularly for the fixed topology case, it is shown that not only the role of each agent is exactly proportional to the value of the corresponding element of ω but also the group decision value can be calculated by such a vector and the initial states of all agents.

Non-linear protocols for optimal distributed consensus in networks of dynamic agents

We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors’ state, but must reach consensus on a group decision value that is function of all the agents’ initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents’ state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents’ initial states. As a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. We use a Lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time-invariant undirected network. Finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles.