Multi-Timescale Distributed Approach to Generalized-Nash-Equilibrium Seeking in Noncooperative Nonconvex Games

<正>Dear Editor,The distributed generalized-Nash-equilibrium(GNE) seeking in noncooperative games with nonconvexity is the topic of this letter.Inspired by the sequential quadratic programming(SQP) method, a multi-timescale multi-agent system(MAS) is developed, and its convergence to a critical point of the game is proven. To illustrate the qualities and efficacy of the theoretical findings, a numerical example is elaborated.     

Necessary Existence Conditions of Weak Equilibria in Noncooperative Differential Programming Games

The necessary existence conditions of active equilibria and maximins are found for noncooperative differential programming games with explicit and implicit relationships between pure and mixed strategies of participants. A technique of search for strategies is presented with the use of an example.     

An Extended Basic System of Equilibria and the Technique of the Solution of Noncooperative Games

A basic system of equilibria for noncooperative games is suggested and studied and the technique of its use is set out for seeking the game equilibria that are most suitable for all players.     

带有预验证机制的区块链动态共识算法

委员会共识和混合共识通过选举委员会来代替全网节点完成区块验证, 可有效加快共识速度, 提高吞吐量, 但恶意攻击和收买易导致委员会发生腐败问题, 严重时将影响共识结果甚至造成系统瘫痪. 现有工作虽引入信誉机制降低委员会节点腐败的可能性, 但开销大、可信度低且无法降低腐败问题对系统的影响. 提出一种带有预验证机制的区块链动态共识算法(DBCP), 通过预验证机制在较小开销的前提下对委员会进行可靠的信誉评估, 及时淘汰委员会中的恶意节点. 若腐败问题已影响到共识结果, DBCP会通过动态共识将区块验证权转移到全网节点, 并淘汰给出错误意见的委员会节点, 避免系统瘫痪. 若委员会通过迭代达到高可信状态, 则DBCP会将区块验证权交由委员会, 全网节点将认同委员会的共识结果, 并不再对区块进行验证, 进而加快共识速度. 经实验验证, DBCP的吞吐量与比特币相比提升了两个数量级, 且与Byzcoin相近, 可在一个出块周期内快速应对委员会腐败问题, 安全性优于Byzcoin.     

基于信誉的动态授权PBFT共识机制

区块链是一种基于零信任基础、去中心化及不可篡改的分布式账本技术。共识算法作为区块链主要技术之一,其效率直接影响区块链系统性能。针对PBFT共识算法运行效率低的问题,本文提出了基于信誉的动态授权PBFT共识机制,引入信誉评价体系对系统节点进行信誉评价,动态决定从信誉最高的节点中选取共识节点,同时实现了非停机情况下动态增删节点的功能,且随着系统长期运行,所能容忍的拜占庭节点动态增加;优化了一致性协议,将传统的一致性协议与基于speculation技术的拜占庭协议进行融合,降低了算力开销和通信代价;通过对共识节点的信誉及行为分析,进一步降低恶意节点成为共识节点的概率,解决了由拜占庭节点作为主节点带来的交易延迟增加问题。最后从算力开销、交易吞吐量和容错性能等方面进行了论证分析。     

Scalable Clock Synchronization Analysis: A Symmetric Noncooperative Output Feedback Tubes-MPC Approach

In the cyber-physical environment, the clock synchronization algorithm is required to have better expansion for network scale. In this paper, a new measurement model of observability under the equivalent transformation of minimum mean square error (MMSE) is constructed based on basic measurement unit (BMU), which can realize the scaled expansion of MMSE measurement. Based on the state updating equation of absolute clock and the decoupled measurement model of MMSE-like equivalence, which is proposed to calculate the positive definite invariant set by using the theoretical-practical Luenberger observer as the synthetical observer, the local noncooperative optimal control problem is built, and the clock synchronization system driven by the ideal state of local clock can reach the exponential convergence for synchronization performance. Different from the problem of general linear system regulators, the state estimation error and state control error are analyzed in the established affine system based on the set-theory-in-control to achieve the quantification of state deviation caused by noise interference. Based on the BMU for isomorphic state map, the synchronization performance of clock states between multiple sets of representative nodes is evaluated, and the scale of evaluated system can be still expanded. After the synchronization is completed, the state of perturbation system remains in the maximum range of measurement accuracy, and the state of nominal system can be stabilized at the ideal state for local clock and realizes the exponential convergence of the clock synchronization system.      

Noncooperative load balancing in distributed systems

In this paper, we present a game theoretic framework for obtaining a user-optimal load balancing scheme in heterogeneous distributed systems. We formulate the static load balancing problem in heterogeneous distributed systems as a noncooperative game among users. For the proposed noncooperative load balancing game, we present the structure of the Nash equilibrium. Based on this structure we derive a new distributed load balancing algorithm. Finally, the performance of our noncooperative load balancing scheme is compared with that of other existing schemes. The main advantages of our load balancing scheme are the distributed structure, low complexity and optimality of allocation for each user.     

均值模型下满足对数级收敛速度的动态系统

文章研究了在均值模型下,动态系统收敛至一致性状态所需的时间。在每一时间步内,节点计算其邻居的均值,并以计算结果作为自己的新值。我们考虑了当节点间的网络结构处于动态变化状态的情况。我们的分析证明了当节点的度在相邻时间点之间变化较小的情况下,即使仅满足微弱的连通性条件,动态变化的网络仍然可以保证动态系统会快速收敛到一致性状态。     

Consensus Control of Multi-Agent Systems Using Fault-Estimation-in-the-Loop: Dynamic Event-Triggered Case

The paper develops a novel framework of consensus control with fault-estimation-in-the-loop for multi-agent systems(MASs) in the presence of faults. A dynamic event-triggered protocol(DETP) by adding an auxiliary variable is utilized to improve the utilization of communication resources. First, a novel estimator with a noise bias is put forward to estimate the existed fault and then a consensus controller with fault compensation(FC) is adopted to realize the demand of reliability and safety of a...     

A New Consensus Algorithm for Multi-Agent Systems via Decentralized Dynamic Output Feedback

In this paper, we study a consensus problem for multi-agent systems via dynamic output feedback control. The entire system is decentralized in the sense that each agent can only obtain output information from its neighbor agents. For practical purpose, we assume that actuator limitation exists, and require that the consensus be achieved among the agents at a specified convergence rate. By using an appropriate coordinate transformation, we reduce the consensus problem on hand to solving a strict matrix inequality, and then propose to use the homotopy based method for solving the matrix inequality. It turns out that our algorithm includes the existing graph Laplacian based algorithm as a special case.     

Dynamic Multi-team Antagonistic Games Model with Incomplete Information and Its Application to Multi-UAV

At present, the studies on multi-team antagonistic games (MTAGs) are still in the early stage, because this complicated problem involves not only incompleteness of information and conflict of interests, but also selection of antagonistic targets. Therefore, based on the previous researches, a new framework is proposed in this paper, which is dynamic multi-team antagonistic games with incomplete information (DMTAGII) model. For this model, the corresponding concept of perfect Bayesian Nash equilibrium (PBNE) is established and the existence of PBNE is also proved. Besides, an interactive iteration algorithm is introduced according to the idea of the best response for solving the equilibrium. Then, the scenario of multiple unmanned aerial vehicles (UAVs) against multiple military targets is studied to solve the problems of tactical decision making based on the DMTAGII model. In the process of modeling, the specific expressions of strategy, status and payoff functions of the games are considered, and the strategy is coded to match the structure of genetic algorithm so that the PBNE can be solved by combining the genetic algorithm and the interactive iteration algorithm. Finally, through the simulation the feasibility and effectiveness of the DMTAGII model are verified. Meanwhile, the calculated equilibrium strategies are also found to be realistic, which can provide certain references for improving the autonomous ability of UAV systems.      

Matrix Resolving Functions in Dynamic Games of Approach

The concept of matrix resolving function is introduced to study dynamic game problems. The sufficient conditions are derived ensuring the possibility for the pursuer to bring the trajectory of a conflict-controlled process to the terminal set. The cases of using quasi-strategies and counter-controls by the pursuer are analyzed separately. Guaranteed times of the game termination for different method’s schemes are compared. The theoretical results are illustrated with a model example of “simple motions” on a plane.     

类Paxos共识算法研究进展

随着互联网数据量和业务量的快速增长,集群规模越来越大,由于机器和网络等故障使得业务中断的可能性越来越高.如何实现一个容错的分布式系统十分重要.多机达成共识是分布式容错系统中一个最基础,最核心的问题.Paxos等一系列共识算法的出现有效地解决了这个问题.近年来,越来越多的系统使用共识相关技术,关于分布式共识算法的研究也层出不穷.这些共识算法可以被划分成2个大类：强领导者共识算法和弱领导者共识算法.随着远程直接内存访问(remote direct memory access, RDMA)等网络技术和现场可编程门阵列(field-programmable gate array, FPGA)等硬件技术的发展,又出现了一些结合新型网络和硬件技术的共识算法研究,用来提升分布式系统的性能.将从分布式共识算法发展历程的角度,介绍Paxos系列算法,阐述算法演进过程中的关键研究,讨论相关算法在不同场景下的优劣势,并展望该类算法的未来发展方向与前景.     

社交网络中舆论共识形成的动态模型分析

本研究致力于深入探讨社交网络中舆论形成的复杂过程,尤其是关注去中心化环境下达成共识的机制.研究提出了一种新的意见分类策略,即第二置信区间.该策略旨在对传统DeGroot共识模型进行改进,从而发展出两种不同的意见动态模型:FAI模型和ORA模型.这些模型综合考虑了个体对周围意见的接受程度和重视程度,并通过对社交网络中邻域意见的深入分析,对个体模型进行了全面设置,涵盖私人意见、表达意见、固执度以及偏好等多重因素.研究结果表明,在特定参数设定下, FAI模型和ORA模型均能比原DeGroot模型更加迅速地达成共识.具体来说, ORA模型的收敛速度在700步长左右,而FAI模型的收敛速度随参数值的增加而逐步接近ORA模型.相较于基准模型, ORA模型在收敛意见值上的差异较小,不超过3.5%,而FAI模型则显示出更大的波动性.这些发现不仅加深了对于社交网络中公共意见形成机制的理解,也强调了个体邻域内意见动力学在共识形成过程中的重要性,为此领域的未来研究提供了新的视角和研究方向.     

Dynamic Games for Stochastic Systems with Delay

This paper discusses dynamic games for a class of linear stochastic delay systems governed by Itô's stochastic differential equation. The Pareto and Nash strategies are developed by solving cross‐coupled matrix inequalities. To obtain these strategy sets, new cross‐coupled algebraic equations (CSAEs) are established on the basis of the Karush‐Kuhn‐Tucker (KKT) conditions, which constitute the necessary conditions. It is noteworthy that the state feedback strategies can be obtained by solving the linear matrix inequality (LMI) recursively. Finally, a numerical example showing the effectiveness of the proposed methods and the attained cost bounds is described.     

Some Practical Approaches to Pursuit-Evasion Dynamic Games

For problems of realistic dynamic games, some practical approaches are proposed to the construction of suboptimal strategies of the behavior of players for different data on the choice of controls by their opponents. All the approaches proposed employ only solvers of one-sided nonlinear optimal control problems and simulation programs. The approaches are as follows: (i) give both players some suboptimal feedback strategies and conduct a great number of Monte Carlo simulations, (ii) give one player a suboptimal feedback strategy and the other player an exact one-sided nonlinear optimal control, (iii) give both players suboptimal feedback strategies dependent on parameters. Each player tries to optimize his parameters with respect to the one-sided nonlinear optimal control of the opponent. Methods (i) and (ii) can be used to solve multi-player problems. The efficiency of the method of choice of a suboptimal strategy is illustrated by examples important for actual practice.     

模糊控制理论在库存货位管理中的应用

针对库存货位布局线性规划的难建模和全重排问题,提出了基于模糊控制理论的库存货位布局方法。在以某公司仓库的实际数据平台基础上,通过选取隶属度函数,建立模糊规则库,进行模糊推理和判决解决了线性规划中存在的问题。重点讨论了模糊控制方法的具体实现步骤。     

Stochastic Dynamic Games with Various Types of Information

Dynamic discrete-time games are generalized to a stochastic environment, in order to examine the influence of various types of information structures on the course of a game. It is shown that the information structure of a game, i.e., type and amount of information available to players and, in particular, asymmetry of information, may lead to unexpected and sometimes counter-intuitive effects on the game result, i.e., the players' payoffs. The paper also develops algorithms for obtaining the Nash equilibrium strategies in such games. These involve reducing optimal reaction policies to the corresponding dynamic programming algorithms and generalizing the classical optimal control technique. Results of computer simulations for a variant of fishery harvesting game are presented.     

Single-Item Dynamic Lot-Sizing Models With Bounded Inventory and Outsourcing

This paper addresses a real-life lot-sizing problem which can be considered a single-item dynamic lot-sizing problem with bounded inventory. The particularity is that the demand of a period can be entirely or partially outsourced with an outsourcing cost. The goal is to minimize the total cost of production, setup, inventory holding, and outsourcing. The cost functions are linear but time-varying. We assume that the unit production cost is constant or nonincreasing over time. The problem is shown to be solvable in a strongly polynomial time with a dynamic-programming approach. The proposed algorithm can solve problems of sizes of up to 400 periods in less than 2 ms on a 1.4-GHz Pentium IV processor.