%0 PDF %T Distributed Dynamic Fusion: Theory and Applications %A Safavi, Sam. %D 2018-03-16T09:33:52.457-04:00 %8 2018-03-16 %R http://localhost/files/vd66wb230 %X Abstract: In this thesis, we study the asymptotic behavior of Linear Time-Varying (LTV) systems that describe fusion in dynamic multi-agent networks. We consider networks that consist of at least one anchor (node with known state) and an arbitrary number of mobile agents that perform a distributed algorithm to achieve a common goal. Due to mobility, the state-update at each agent depends on the availability of neighbors. Agent mobility, thus, leads to an LTV abstraction where the system matrices are random, and can be either stochastic, if the neighborhood at the updating agent does not contain any anchor, or, sub-stochastic, if the neighborhood contains anchors. We refer to the general class of such time-varying fusion algorithms over mobile agents as Distributed Dynamic Fusion (DDF). In this context, we study the conditions required on the DDF system matrices such that the dynamic fusion forgets the initial conditions and converges to (a linear combination of) the anchor state(s). To this aim, we partition the sequence of system matrices into non-overlapping slices, and by introducing the notion of unbounded connectivity, we obtain stability conditions in terms of the slice lengths and some network parameters. In particular, we show that the system is asymptotically stable if the unbounded lengths of an infinite subset of slices grow slower than an explicit exponential rate. We apply the DDF theory in the design and analysis of the following distributed algorithms: (i) dynamic leader-follower; and (ii) localization in dynamic multi-agent networks. We first consider dynamic leader-follower problem, where the goal for the entire network is to converge to the state of a leader. We assume that at each iteration, one agent exchanges information with nearby nodes and updates its state as a linear-convex combination of the neighboring states. We develop the conditions under which the underlying (sub-) stochastic LTV system converges to the leader state regardless of the agents' initial conditions. We then consider localization in mobile multi-agent networks. We provide a distributed algorithm to localize an arbitrary number of agents moving in a bounded region of interest. In the case of such mobile networks, the main challenge is that the agents may not be able to find nearby agents to implement a distributed algorithm. We address this issue by providing an opportunistic algorithm that only implements a linear-convex location update when it lies inside the convex hull of nearby agents and does not update otherwise. We abstract this algorithm as an LTV system, whose system matrices may be stochastic, or sub-stochastic, intermittently, and provide sufficient conditions for the network to track the agents' true locations. By introducing the notion of virtual convex hull, we provide an alternative localization algorithm that does not require an agent to lie inside the convex of the neighbors at any given time. We investigate the effects of noise on both localization algorithms and provide modifications to counter the undesirable effects of noise. Finally, we relate the dimension of motion in the network to the number of anchors required, and show that a network of mobile agents with full degrees of freedom in the motion can be localized precisely, as long as there is at least one anchor in the network. To the best of our knowledge, this is a unique property that distinguishes the proposed localization approach in this thesis from the existing algorithms in the literature.; Thesis (Ph.D.)--Tufts University, 2017.; Submitted to the Dept. of Electrical Engineering.; Advisor: Usman Khan.; Committee: Jason Rife, Brian Tracey, and Jose Bento.; Keyword: Electrical engineering. %[ 2022-10-11 %9 Text %~ Tufts Digital Library %W Institution