58,663 research outputs found
Accelerating Consensus by Spectral Clustering and Polynomial Filters
It is known that polynomial filtering can accelerate the convergence towards
average consensus on an undirected network. In this paper the gain of a
second-order filtering is investigated. A set of graphs is determined for which
consensus can be attained in finite time, and a preconditioner is proposed to
adapt the undirected weights of any given graph to achieve fastest convergence
with the polynomial filter. The corresponding cost function differs from the
traditional spectral gap, as it favors grouping the eigenvalues in two
clusters. A possible loss of robustness of the polynomial filter is also
highlighted
Robust â„‹2 Performance: Guaranteeing Margins for LQG Regulators
This paper shows that ℋ2 (LQG) performance specifications can be combined with structured uncertainty in the system, yielding robustness analysis conditions of the same nature and computational complexity as the corresponding conditions for ℋ∞ performance. These conditions are convex feasibility tests in terms of Linear Matrix Inequalities, and can be proven to be necessary and sufficient under the same conditions as in the ℋ∞ case.
With these results, the tools of robust control can be viewed as coming full circle to treat the problem where it all began: guaranteeing margins for LQG regulators
Task-Driven Estimation and Control via Information Bottlenecks
Our goal is to develop a principled and general algorithmic framework for
task-driven estimation and control for robotic systems. State-of-the-art
approaches for controlling robotic systems typically rely heavily on accurately
estimating the full state of the robot (e.g., a running robot might estimate
joint angles and velocities, torso state, and position relative to a goal).
However, full state representations are often excessively rich for the specific
task at hand and can lead to significant computational inefficiency and
brittleness to errors in state estimation. In contrast, we present an approach
that eschews such rich representations and seeks to create task-driven
representations. The key technical insight is to leverage the theory of
information bottlenecks}to formalize the notion of a "task-driven
representation" in terms of information theoretic quantities that measure the
minimality of a representation. We propose novel iterative algorithms for
automatically synthesizing (offline) a task-driven representation (given in
terms of a set of task-relevant variables (TRVs)) and a performant control
policy that is a function of the TRVs. We present online algorithms for
estimating the TRVs in order to apply the control policy. We demonstrate that
our approach results in significant robustness to unmodeled measurement
uncertainty both theoretically and via thorough simulation experiments
including a spring-loaded inverted pendulum running to a goal location.Comment: 9 pages, 4 figures, abridged version accepted to ICRA2019;
Incorporates changes in final conference submissio
Witnesses of causal nonseparability: an introduction and a few case studies
It was recently realised that quantum theory allows for so-called causally
nonseparable processes, which are incompatible with any definite causal order.
This was first suggested on a rather abstract level by the formalism of process
matrices, which only assumes that quantum theory holds locally in some
observers' laboratories, but does not impose a global causal structure; it was
then shown, on a more practical level, that the quantum switch---a new resource
for quantum computation that goes beyond causally ordered circuits---provided
precisely a physical example of a causally nonseparable process. To demonstrate
that a given process is causally nonseparable, we introduced in [Ara\'ujo et
al., New J. Phys. 17, 102001 (2015)] the concept of witnesses of causal
nonseparability. Here we present a shorter introduction to this concept, and
concentrate on some explicit examples to show how to construct and use such
witnesses in practice.Comment: 15 pages, 7 figure
Optimized pulses for the control of uncertain qubits
Constructing high-fidelity control fields that are robust to control, system,
and/or surrounding environment uncertainties is a crucial objective for quantum
information processing. Using the two-state Landau-Zener model for illustrative
simulations of a controlled qubit, we generate optimal controls for \pi/2- and
\pi-pulses, and investigate their inherent robustness to uncertainty in the
magnitude of the drift Hamiltonian. Next, we construct a quantum-control
protocol to improve system-drift robustness by combining environment-decoupling
pulse criteria and optimal control theory for unitary operations. By
perturbatively expanding the unitary time-evolution operator for an open
quantum system, previous analysis of environment-decoupling control pulses has
calculated explicit control-field criteria to suppress environment-induced
errors up to (but not including) third order from \pi/2- and \pi-pulses. We
systematically integrate this criteria with optimal control theory,
incorporating an estimate of the uncertain parameter, to produce improvements
in gate fidelity and robustness, demonstrated via a numerical example based on
double quantum dot qubits. For the qubit model used in this work, post facto
analysis of the resulting controls suggests that realistic control-field
fluctuations and noise may contribute just as significantly to gate errors as
system and environment fluctuations.Comment: 38 pages, 15 figures, RevTeX 4.1, minor modifications to the previous
versio
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