Electrical & Computer Engineering
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Item GENERALIZED DISTRIBUTED CONSENSUS-BASED ALGORITHMS FOR UNCERTAIN SYSTEMS AND NETWORKS(2010) Matei, Ion; Baras, John S; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)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 consensusbased 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.Item NONLINEAR DETECTION, ESTIMATION, AND CONTROL FOR FREE-SPACE OPTICAL COMMUNICATION(2008-08-01) Komaee, Arash; Krishnaprasad, P. S.; Narayan, Prakash; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In free-space optical communication, the intensity of a laser beam is modulated by a message, the beam propagates through free-space or atmosphere, and eventually strikes the receiver. At the receiver, an optical sensor converts the optical energy into an electrical signal, which is processed to reconstruct the original message. The promising features of this communication scheme such as high-bandwidth, power efficiency, and security, render it a viable means for high data rate point-to-point communication. In this dissertation, we adopt a stochastic approach to address two major issues associated with free-space optics: digital communication over an atmospheric channel and maintaining optical alignment between the transmitter and the receiver, in spite of their relative motion. Associated with these issues, we consider several detection, estimation, and optimal control problems with point process observations. Although these problems are motivated by applications in free-space optics, they are also of direct relevance to the general field of estimation theory and stochastic control. We study the detection aspect of digital communication over an atmospheric channel. This problem is formulated as an M-ary hypothesis testing problem involving a doubly stochastic marked and filtered Poisson process in white Gaussian noise. The formal solutions we obtain for this problem are hard to express in an explicit form, thus we approximate them by appropriate closed form expressions. These approximations can be implemented using finite-dimensional, nonlinear, causal filters. Regarding the optical alignment issue, we consider two problems: active pointing and cooperative optical beam tracking. In the active pointing scheme that we develop for short range applications, the receiving station estimates the center of its incident optical beam based on the output of a position-sensitive photodetector. The transmitter receives this estimate via an independent communication link and incorporates it to accurately aim at the receiving station. A cooperative optical beam tracking system consists of two stations in such a manner that each station points its optical beam toward the other one. The stations employ the arrival direction of the incident optical beams as a guide to precisely point their own beam toward the other station. We develop a detailed stochastic model for this system and employ it to determine a control law which maximizes the flow of optical energy between the stations. In so doing, we consider the effect of light propagation delay, which requires a point-ahead mechanism to compensate for the displacement of the receiving station during propagation time.