Distributed Dynamic Fusion: Theory and Applications
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 t... read morehe 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.read less