2,191 research outputs found
Distributed tracking control of leader-follower multi-agent systems under noisy measurement
In this paper, a distributed tracking control scheme with distributed
estimators has been developed for a leader-follower multi-agent system with
measurement noises and directed interconnection topology. It is supposed that
each follower can only measure relative positions of its neighbors in a noisy
environment, including the relative position of the second-order active leader.
A neighbor-based tracking protocol together with distributed estimators is
designed based on a novel velocity decomposition technique. It is shown that
the closed loop tracking control system is stochastically stable in mean square
and the estimation errors converge to zero in mean square as well. A simulation
example is finally given to illustrate the performance of the proposed control
scheme.Comment: 8 Pages, 3 figure
Convergence Rate Analysis of Distributed Gossip (Linear Parameter) Estimation: Fundamental Limits and Tradeoffs
The paper considers gossip distributed estimation of a (static) distributed
random field (a.k.a., large scale unknown parameter vector) observed by
sparsely interconnected sensors, each of which only observes a small fraction
of the field. We consider linear distributed estimators whose structure
combines the information \emph{flow} among sensors (the \emph{consensus} term
resulting from the local gossiping exchange among sensors when they are able to
communicate) and the information \emph{gathering} measured by the sensors (the
\emph{sensing} or \emph{innovations} term.) This leads to mixed time scale
algorithms--one time scale associated with the consensus and the other with the
innovations. The paper establishes a distributed observability condition
(global observability plus mean connectedness) under which the distributed
estimates are consistent and asymptotically normal. We introduce the
distributed notion equivalent to the (centralized) Fisher information rate,
which is a bound on the mean square error reduction rate of any distributed
estimator; we show that under the appropriate modeling and structural network
communication conditions (gossip protocol) the distributed gossip estimator
attains this distributed Fisher information rate, asymptotically achieving the
performance of the optimal centralized estimator. Finally, we study the
behavior of the distributed gossip estimator when the measurements fade (noise
variance grows) with time; in particular, we consider the maximum rate at which
the noise variance can grow and still the distributed estimator being
consistent, by showing that, as long as the centralized estimator is
consistent, the distributed estimator remains consistent.Comment: Submitted for publication, 30 page
Causal categories: relativistically interacting processes
A symmetric monoidal category naturally arises as the mathematical structure
that organizes physical systems, processes, and composition thereof, both
sequentially and in parallel. This structure admits a purely graphical
calculus. This paper is concerned with the encoding of a fixed causal structure
within a symmetric monoidal category: causal dependencies will correspond to
topological connectedness in the graphical language. We show that correlations,
either classical or quantum, force terminality of the tensor unit. We also show
that well-definedness of the concept of a global state forces the monoidal
product to be only partially defined, which in turn results in a relativistic
covariance theorem. Except for these assumptions, at no stage do we assume
anything more than purely compositional symmetric-monoidal categorical
structure. We cast these two structural results in terms of a mathematical
entity, which we call a `causal category'. We provide methods of constructing
causal categories, and we study the consequences of these methods for the
general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure
Optimal Two Player LQR State Feedback With Varying Delay
This paper presents an explicit solution to a two player distributed LQR
problem in which communication between controllers occurs across a
communication link with varying delay. We extend known dynamic programming
methods to accommodate this varying delay, and show that under suitable
assumptions, the optimal control actions are linear in their information, and
that the resulting controller has piecewise linear dynamics dictated by the
current effective delay regime.Comment: Extended version of IFAC '14 submissio
A universe of processes and some of its guises
Our starting point is a particular `canvas' aimed to `draw' theories of
physics, which has symmetric monoidal categories as its mathematical backbone.
In this paper we consider the conceptual foundations for this canvas, and how
these can then be converted into mathematical structure. With very little
structural effort (i.e. in very abstract terms) and in a very short time span
the categorical quantum mechanics (CQM) research program has reproduced a
surprisingly large fragment of quantum theory. It also provides new insights
both in quantum foundations and in quantum information, and has even resulted
in automated reasoning software called `quantomatic' which exploits the
deductive power of CQM. In this paper we complement the available material by
not requiring prior knowledge of category theory, and by pointing at
connections to previous and current developments in the foundations of physics.
This research program is also in close synergy with developments elsewhere, for
example in representation theory, quantum algebra, knot theory, topological
quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World
through Mathematical Innovation", H. Halvorson, ed., Cambridge University
Press, forthcoming. (as usual, many pictures
Positivity of Lyapunov exponents for Anderson-type models on two coupled strings
We study two models of Anderson-type random operators on two
deterministically coupled continuous strings. Each model is associated with
independent, identically distributed four-by-four symplectic transfer matrices,
which describe the asymptotics of solutions. In each case we use a criterion by
Gol'dsheid and Margulis (i.e. Zariski denseness of the group generated by the
transfer matrices in the group of symplectic matrices) to prove positivity of
both leading Lyapunov exponents for most energies. In each case this implies
almost sure absence of absolutely continuous spectrum (at all energies in the
first model and for sufficiently large energies in the second model). The
methods used allow for singularly distributed random parameters, including
Bernoulli distributions.Comment: 19 page
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