Cycle Flow Formulation of Optimal Network Flow Problems and Respective Distributed Solutions

In this paper, we use the cycle basis from graph theory to reduce the size of the decision variable space of optimal network flow problems by eliminating the aggregated flow conservation constraint. We use a minimum cost flow problem and an optimal power flow problem with generation and storage at the nodes to demonstrate our decision variable reduction method. The main advantage of the proposed technique is that it retains the natural sparse/decomposable structure of network flow problems. As such, the reformulated problems are still amenable to distributed solutions. We demonstrate this by proposing a distributed alternating direction method of multipliers (ADMM) solution for a minimum cost flow problem. We also show that the communication cost of the distributed ADMM algorithm for our proposed cycle-based formulation of the minimum cost flow problem is lower than that of a distributed ADMM algorithm for the original arc-based formulation.      

Distributed cooperative learning algorithms using wavelet neural network

This paper investigates the distributed cooperative learning (DCL) problems over networks, where each node only has access to its own data generated by the unknown pattern (map or function) uniformly, and all nodes cooperatively learn the pattern by exchanging local information with their neighboring nodes. These problems cannot be solved by using traditional centralized algorithms. To solve these problems, two novel DCL algorithms using wavelet neural networks are proposed, including continuous-time DCL (CT-DCL) algorithm and discrete-time DCL (DT-DCL) algorithm. Combining the characteristics of neural networks with the properties of the wavelet approximation, the wavelet series are used to approximate the unknown pattern. The DCL algorithms are used to train the optimal weight coefficient matrix of wavelet series. Moreover, the convergence of the proposed algorithms is guaranteed by using the Lyapunov method. Compared with existing distributed optimization strategies such as distributed average consensus (DAC) and alternating direction method of multipliers (ADMM), our DT-DCL algorithm requires less information communications and training time than ADMM strategy. In addition, it achieves higher accuracy than DAC strategy when the network consists of large amounts of nodes. Moreover, the proposed CT-DCL algorithm using a proper step size is more accurate than the DT-DCL algorithm if the training time is not considered. Several illustrative examples are presented to show the efficiencies and advantages of the proposed algorithms.

     

基于无网格压缩感知的DOA估计算法

应用传统的压缩感知理论对天线阵列信号的波达方向(Direction-of-arrival,DOA) 进行估计,存在基的失配问题。基于交替方向乘子法 (Alternative Direction Method of Multiplier,ADMM) 的无网格压缩感知(Grid-less Compressive Sensing) 技术能够解决该问题,但仍存在收敛速度慢的缺陷。针对该缺陷, 提出带自适应惩罚项的ADMM (ADMM with adaptive penalty,AP-ADMM)算法,即根据输入信号的噪声功率,自适应地选择惩罚项的初始值;同时在算法迭代求解的过程中,自适应地对目标函数的惩罚项进行调整。与传统算法相比,在保证收敛精度和DOA的恢复成功概率的条件下,带自适应惩罚项的ADMM算法收敛速率明显加快。仿真结果验证了新算法的有效性。     

Distributed optimisation for multi-agent systems with the first-order integrals under Markovian switching topologies

This paper studies the distributed optimisation problem for multi-agent systems with the first-order dynamics over Markovian switching topologies. The interaction topology among agents’ switches following a Markov process and each topology is modelled as a state of the Markov process. The aim is to minimise the global cost functions and make the agents converge to the optimal point through the network communication between the agents, where each agent has a local convex cost function only known by itself. Utilising the knowledge of convex analysis and graph theory, we establish a distributed algorithm for the optimisation problem with randomly switching topologies. A sufficient condition for the existence of such algorithm is obtained by using the Lyapunov method. Besides, the result is also extended to the cases of a Markov process with partially unknown transition rates. Finally, numerical simulations are given to validate the proposed algorithm.     

非光滑聚合博弈纳什均衡的分布式连续时间算法

本文研究多智能体聚合博弈的分布式算法设计.其中,个体的成本函数具有非光滑性.提出一个连续时间分布式算法,使得每个个体仅利用本地数据及局部的信息交互就能达到纳什均衡.利用李雅普诺夫方法,证明了算法的收敛性.在此基础上,进一步研究了带有耦合不等式约束博弈的广义纳什均衡求解.仿真结果验证了方法的有效性.     

Distributed envy minimization for resource allocation

Minimizing envy in distributed discrete resource or task allocation, is an unusual distributed optimization challenge, since the quality of the allocation for each of the agents is dependent, not only on its own allocation, but on the allocation of others as well. Thus, in order to perform distributed search for allocations with minimal envy there is a need to design innovative algorithms that can cope with the challenging constraint structure of an envy minimization problem. Distributed methods for minimizing envy among agents in indivisible resource allocation problems are presented. First, Distributed Envy Minimization Problems (DEMP) are formulated as Distributed Constraint Reasoning problems. When the DEMPs are large, and cannot be solved by a complete search an incomplete local search algorithm is presented. Each transfer of a good from one agent to another involves the change of state of more than one agent. Thus, a minimizing envy local search algorithm must build upon actions (transfers) that include multiple agents. Since DEMPs are particularly susceptible to local minima during local search, the paper proposes an algorithm that alternates between two different hill climbing search phases. The first phase uses one-transfer steps while the other exploits envy cycle elimination steps. An algorithm that minimizes envy while preserving efficiency, is proposed. The proposed algorithm finds a Pareto optimal allocation with low envy. In the context of resource allocation problems, a Pareto optimal solution is particularly desirable since it presents a stable solution. The proposed algorithm first finds a divisible Pareto optimal envy-free allocation using a Fisher market equilibrium. This allocation is transferred into an indivisible allocation of goods while maintaining the Pareto optimal characteristic of the allocation and a low envy level among agents.     

A solution strategy for distributed uncertain economic dispatch problems via scenario theory

In this paper, an uncertain economic dispatch problem (EDP) is considered for a group of coopertive agents. First, let each agent extract a set of samples (scenarios) from the uncertain set, and then a scenario EDP is obtained using these scenarios. Based on the scenario theory, a prior certification is provided to evaluate the probabilistic feasibility of the scenario solution for uncertain EDP. To facilitate the computational task, a distributed solution strategy is proposed by the alternating direction method of multipliers (ADMM) and a finite-time consensus strategy. Moreover, the distributed strategy can solve the scenario problem over a weight-balanced directed graph. Finally, the proposed solution strategy is applied to an EDP for a power system involving wind power plants.     

基于鞍点法的自适应分布式资源分配算法

研究一类带有不等式约束为凸函数的多智能体系统分布式资源分配问题.在资源分配问题中,各智能体拥有仅自身可知的局部成本函数和局部凸不等式约束.分布式资源分配旨在如何利用智能体间的信息交互设计一种分布式优化算法,完成定量资源分配的同时还保证最小化全局成本函数.针对该问题,基于卡罗需-库恩-塔克条件和比例积分控制思想,首先提出一种自适应分布式优化算法,其中凸不等式约束的对偶变量可实现自适应获取;然后,为了降低系统的通信资源消耗,设计一种动态事件触发控制策略以实现离散时间通信的分布式资源分配算法;最后,通过数值仿真验证所设计算法的有效性.     

基于交替方向乘子法的电力系统完全分布式动态经济调度方法

本文基于交替方向乘子法(alternating direction multiplier method,ADMM)提出了一种完全分布式的跨区域电力系统动态经济调度方法.其中的经济调度模型以整个系统的运行成本最小为目标,并满足各种系统运行约束.为了实现模型的分布式求解,本文利用交替方向乘子法将各区域之间的联系解耦,将整个系统的大型优化问题分解为各个区域内部的子优化问题,通过迭代求解每个区域的子问题即可得到整个系统的最优解.进一步地,本文算法取消了负责乘子更新的数据中心,实现了完全分布式的调度策略.同时,为了兼顾电力系统中时间断面之间的紧密联系,本文的经济调度模型采用了多时段优化方法.最后,本文对基于IEEE标准测试系统的3区域互联系统算例进行了分析,验证了本文的调度策略的有效性.     

基于自适应精确罚函数的分布式资源分配算法

在多智能体系统中, 分布式资源分配问题是近年来研究热点之一. 分布式资源分配问题旨在通过智能体间信息交互实现资源最优配置. 其中智能体局部约束给算法设计带来巨大挑战. 首先, 针对一阶多智能体系统, 提出基于自适应精确罚函数的分布式资源分配算法, 其中各智能体利用距离函数实现局部约束求解. 此外, 自适应设计思想旨在避免算法对全局先验知识获取. 其次, 利用跟踪技术实现二阶多智能体系统算法设计. 并利用凸函数和非光滑分析法给出严谨的收敛性分析. 最后, 仿真结果验证了本文所设计优化算法对强凸分布式资源分配问题的有效性.     

有适应力的分布式状态估计方法

为提高智能体系统对攻击的免疫力,研究了测量攻击下的适应力分布式状态估计方法。每个智能体对系统状态进行连续的本地线性测量。由于不同智能体的本地测量模型相互异构,对系统状态可能不具有本地可观测性,且攻击者能够操控部分智能体的测量数据,随意改变其测量结果。而智能体的目标是协同处理本地测量数据,并正确估计出未知的系统状态。因此,该问题的挑战在于在不对真实测量数据和恶意智能体的测量数据进行分辨时,如何设计算法估计得到真实的系统状态。为了解决这个问题,设计了适应性分布式最大后验概率估计算法。在该算法中,只要恶意智能体的数量小于某个特定值,所有智能体都能够收敛到系统状态。首先,根据卡尔曼滤波给出集中式最大后验概率(Maximum A Posteriori, MAP)估计方法,并与分布式一致性结合,进而得到分布式最大后验概率估计方法。然后,考虑到测量攻击,从估计一致性的角度,利用自适应饱和度增益设计了适应性分布式最大后验概率估计方法。最后,通过仿真实验验证算法的有效性。     

一阶多智能体受扰系统的自抗扰分布式优化算法

研究一类具有未知外部干扰的一阶多智能体系统的分布式优化问题.在分布式优化任务中,每个智能体只被容许利用自己的局部目标函数和邻居的状态信息,设计一个分布式优化算法,使全局目标函数取得最小值,其中全局目标函数是所有局部目标函数之和.针对该问题,首先提出由扩张状态观测器和优化算法组成的自抗扰分布式优化算法.其次,在Lyapu...     

Precoder design in downlink CoMP-JT MIMO network via WMMSE and asynchronous ADMM

Precoder design of coordinated multi-point joint transmission (CoMP-JT) multiple-input and multiple-output (MIMO) network aimied at throughput maximization is a challenging problem. In this paper, we propose an asynchronous distributed iterative method to solve this problem. We transform the original throughput maximizing problem to the weighted minimum mean square error (WMMSE) problem, then decompose the problem into a series of subproblems. Based on alternation direction method of multipliers (ADMM), the proposed algorithm can solve the optimal precoder in a distributed manner. With asynchronous information exchange mechanism considered, the convergence rate of our algorithm can be accelerated further. Numerical results demonstrate the increase of throughput and the optimality of the precoding scheme provided by our algorithm.     

多智能体系统中基于局部测量信息的目标定位

针对多智能体系统中的定位问题,设计一种在变拓扑网络条件下的分布式目标定位算法,使所有智能体实现目标的相对定位.假设智能体只能获取局部的测量信息并进行局部信息交换.算法包括成对智能体之间相互定位算法和基于一致性的目标定位融合算法,对算法的成立条件和收敛误差进行分析,并通过仿真实验验证所提出算法的有效性.     

Distributed connected coverage control for groups of mobile agents

For a group of mobile agents, each agent can sense the local environment around it and directly communicate with others in its communication range. This article deals with the self-deployment problem of mobile agents to achieve a sensing coverage over the environment as large as possible, while keeping the underlying time-variant communication topology connected all the time. For this problem, a self-deployment algorithm is developed for each agent. It guarantees network connectivity by preserving the group core structure, which is extracted from the communication topology in a completely distributed, local manner and is renewed in each iteration period. Note that maintaining all the connecting edges in the core structure still remains a sufficient degree of freedom for each agent to traverse over a maximal distance from its neighbours. Thus, the distributed connected coverage objective can be achieved by spreading out the group members with the constraints of preserving the core structure. The performance of the self-deployment algorithm is demonstrated by both theoretical analysis and numerical simulations.     

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions

This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state information with its current neighbors through a time-varying digraph. In addition, the agents do not have access to the information about the current cost functions until decisions are made. Different from most existing works on online distributed optimization, here we consider the case where the cost functions are strongly pseudoconvex and real gradients of the cost functions are not available. To handle this problem, a random gradient-free online distributed algorithm involving the multi-point gradient estimator is proposed. Of particular interest is that under the proposed algorithm, each agent only uses the estimation information of gradients instead of the real gradient information to make decisions. The dynamic regret is employed to measure the proposed algorithm. We prove that if the cumulative deviation of the minimizer sequence grows within a certain rate, then the expectation of dynamic regret increases sublinearly. Finally, a simulation example is given to corroborate the validity of our results.     

分布式在线交替方向乘子法

针对如何对分布式网络采集的数据进行在线学习的问题,提出了一种基于交替方向乘子法(ADMM)的分布式在线学习优化算法--分布式在线交替方向乘子法(DOM)。首先,针对分布式在线学习需要各节点根据新采集的数据来更新本地估计,同时保持网络中所有节点的估计趋于一致这一问题,建立了数学模型并设计DOM算法对其进行求解。其次,针对分布式在线学习问题定义了Regret 界,用以表征在线估计的性能;证明了当本地即时损失函数是凸函数时,DOM算法是收敛的,并给出了其收敛速度。最后,通过数值仿真实验结果表明,相比现有的分布式在线梯度下降法(DOGD)和分布式在线自主学习算法(DAOL),所提出的DOM算法具有更快的收敛性能。     

Multiagent task allocation in social networks

This paper proposes a new variant of the task allocation problem, where the agents are connected in a social network and tasks arrive at the agents distributed over the network. We show that the complexity of this problem remains NP-complete. Moreover, it is not approximable within some factor. In contrast to this, we develop an efficient greedy algorithm for this problem. Our algorithm is completely distributed, and it assumes that agents have only local knowledge about tasks and resources. We conduct a broad set of experiments to evaluate the performance and scalability of the proposed algorithm in terms of solution quality and computation time. Three different types of networks, namely small-world, random and scale-free networks, are used to represent various social relationships among agents in realistic applications. The results demonstrate that our algorithm works well and also that it scales well to large-scale applications. In addition we consider the same problem in a setting where the agents holding the resources are self-interested. For this, we show how the optimal algorithm can be used to incentivize these agents to be truthful. However, the efficient greedy algorithm cannot be used in a truthful mechanism, therefore an alternative, cluster-based algorithm is proposed and evaluated.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

Distributed robust MPC for nonholonomic robots with obstacle and collision avoidance

Considering that the inevitable disturbances and coupled constraints pose an ongoing challenge to distributed control algorithms, this paper proposes a distributed robust model predictive control (MPC) algorithm for a multi-agent system with additive external disturbances and obstacle and collision avoidance constraints. In particular, all the agents are allowed to solve optimization problems simultaneously at each time step to obtain their control inputs, and the obstacle and collision avoidance are accomplished in the context of full-dimensional controlled objects and obstacles. To achieve the collision avoidance between agents in the distributed framework, an assumed state trajectory is introduced for each agent which is transmitted to its neighbors to construct the polyhedral over-approximations of it. Then the polyhedral over-approximations of the agent and the obstacles are used to smoothly reformulate the original nonconvex obstacle and collision avoidance constraints. And a compatibility constraint is designed to restrict the deviation between the predicted and assumed trajectories. Moreover, recursive feasibility of each local MPC optimization problem with all these constraints derived and input-to-state stability of the closed-loop system can be ensured through a sufficient condition on controller parameters. Finally, simulations with four agents and two obstacles demonstrate the efficiency of the proposed algorithm.