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Generalized distributed consensus-based algorithms for uncertain systems and networks.

机译：不确定系统和网络的基于分布式共识的广义算法。

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摘要

We address four problems related to multi-agent optimization, filtering and agreement. First, we investigate collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensus-based multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents' estimates of the optimal decision vector, and the optimal value. In addition, for a particular class of convex functions, we give an upper bound on the distances between the agents' estimates of the optimal decision vector and the minimizer and we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application, we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols.;Second, we generalize the asymptotic consensus problem to convex metric spaces. Under minimal connectivity assumptions, we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the generalized convex hull generated by the agents current state and the states of its neighbors, then agreement is achieved asymptotically. In addition, we give bounds on the distance between the consensus point(s) and the initial values of the agents. As an application example, we introduce a probabilistic algorithm for reaching consensus of opinion and show that it in fact fits our general framework.;Third, we discuss the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state, Markov process, each topology corresponding to a state of the process. We address both the cases where the dynamics of the agents are expressed in continuous and discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square and almost sure senses if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected.;Fourth, we address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) are asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations. We continue by presenting a connection between the consensus-based distributed linear filter and the optimal linear filter of a Markovian jump linear system, appropriately defined. More specifically, we show that if the Markovian jump linear system is (mean square) detectable, then the stochastic process is detectable under the consensus-based distributed linear filtering scheme. We also show that the optimal gains of a linear filter for estimating the state of a Markovian jump linear system, appropriately defined, can be used to approximate the optimal gains of the consensus-based linear filter.
机译：我们解决了与多主体优化，过滤和协议相关的四个问题。首先，当代理使用本地信息以分布式方式做出决策时，我们研究目标函数的优化表示为局部凸函数之和，而用于交换消息和信息的通信拓扑是由图值随机模型建模的过程，假定是独立的并且分布均匀。具体来说，我们研究了基于共识的多主体分布式次梯度方法的性能，并展示了它如何依赖于随机图的概率分布。对于恒定步长的情况，我们首先给出目标函数之间的差异上限，该目标函数是由代理对最佳决策向量的估计值和最佳值进行评估的。另外，对于一类特殊的凸函数，我们给出了代理对最佳决策向量的估计与最小化器之间的距离的上限，并提供了收敛速度为上述上限的时变分量为零的结果。界。寻址指标通过其预期值进行评估。作为一个应用，我们展示了如何使用分布式优化算法来进行协同系统识别，并在随机和广播八卦协议下提供了数值实验。第二，将渐近共识问题推广到凸度量空间。在最小连通性假设下，我们表明，如果代理在每次迭代中都通过从代理当前状态及其邻居的状态生成的广义凸包的特定子集中选择一个点来更新其状态，则可以渐近地达成一致。此外，我们给出了共识点与代理初始值之间的距离界限。作为一个应用实例，我们介绍了一种达成共识的概率算法，并证明它实际上符合我们的一般框架。第三，讨论了动态主体网络的线性渐近共识问题，该网络的通信网络是随机建模的。切换图。切换由有限状态的马尔可夫过程确定，每个拓扑对应于过程的状态。我们处理两种情况，即代理的动态性以连续和离散时间表示。我们证明，如果共识矩阵是双重随机的，则在且仅当由与马尔可夫过程的状态相对应的图的并集产生的图紧密相连时，才能在均方和几乎肯定的意义上实现平均共识。 ，我们解决了基于共识的分布式线性滤波问题，其中传感器网络观察到了离散时间，线性随机过程。我们假设共识权重是已知的，并且我们首先提供了可以检测到随机过程的充分条件，即，对于共识权重的特定选择，存在一组滤波增益，使得估计误差的动态性（无噪声）为渐近稳定。接下来，我们基于最小化二次滤波成本的上限，开发了一种分布式次优滤波方案。在平稳情况下，我们提供了该方案收敛的充分条件；条件是根据一组耦合的Riccati方程的收敛性表示的。我们继续介绍适当地定义的基于共识的分布式线性滤波器和马尔可夫跳跃线性系统的最佳线性滤波器之间的联系。更具体地，我们表明，如果马尔可夫跳跃线性系统是（均方）可检测的，那么在基于共识的分布式线性滤波方案下随机过程是可检测的。我们还表明，适当估计的用于估计马氏跳跃线性系统状态的线性滤波器的最佳增益可用于近似基于共识的线性滤波器的最佳增益。

著录项

  • 作者

    Matei, Ion.;

  • 作者单位

    University of Maryland, College Park.;

  • 授予单位 University of Maryland, College Park.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 176 p.
  • 总页数 176
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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