8,077 research outputs found
Consensus Computation in Unreliable Networks: A System Theoretic Approach
This work addresses the problem of ensuring trustworthy computation in a
linear consensus network. A solution to this problem is relevant for several
tasks in multi-agent systems including motion coordination, clock
synchronization, and cooperative estimation. In a linear consensus network, we
allow for the presence of misbehaving agents, whose behavior deviate from the
nominal consensus evolution. We model misbehaviors as unknown and unmeasurable
inputs affecting the network, and we cast the misbehavior detection and
identification problem into an unknown-input system theoretic framework. We
consider two extreme cases of misbehaving agents, namely faulty (non-colluding)
and malicious (Byzantine) agents. First, we characterize the set of inputs that
allow misbehaving agents to affect the consensus network while remaining
undetected and/or unidentified from certain observing agents. Second, we
provide worst-case bounds for the number of concurrent faulty or malicious
agents that can be detected and identified. Precisely, the consensus network
needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to
be generically detectable and identifiable by every well behaving agent. Third,
we quantify the effect of undetectable inputs on the final consensus value.
Fourth, we design three algorithms to detect and identify misbehaving agents.
The first and the second algorithm apply fault detection techniques, and
affords complete detection and identification if global knowledge of the
network is available to each agent, at a high computational cost. The third
algorithm is designed to exploit the presence in the network of weakly
interconnected subparts, and provides local detection and identification of
misbehaving agents whose behavior deviates more than a threshold, which is
quantified in terms of the interconnection structure
Computational linear algebra over finite fields
We present here algorithms for efficient computation of linear algebra
problems over finite fields
Eigenvalues of rank one perturbations of unstructured matrices
Let be a fixed complex matrix and let be two vectors. The
eigenvalues of matrices form a system
of intersecting curves. The dependence of the intersections on the vectors
is studied
Critical manifolds and stability in Hamiltonian systems with non-holonomic constraints
We explore a particular approach to the analysis of dynamical and geometrical
properties of autonomous, Pfaffian non-holonomic systems in classical
mechanics. The method is based on the construction of a certain auxiliary
constrained Hamiltonian system, which comprises the non-holonomic mechanical
system as a dynamical subsystem on an invariant manifold. The embedding system
possesses a completely natural structure in the context of symplectic geometry,
and using it in order to understand properties of the subsystem has compelling
advantages. We discuss generic geometric and topological properties of the
critical sets of both embedding and physical system, using Conley-Zehnder
theory and by relating the Morse-Witten complexes of the 'free' and constrained
system to one another. Furthermore, we give a qualitative discussion of the
stability of motion in the vicinity of the critical set. We point out key
relations to sub-Riemannian geometry, and a potential computational
application.Comment: LaTeX, 52 pages. Sections 2 and 3 improved, Section 5 adde
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