673 research outputs found
Nonparametric Infinite Horizon Kullback-Leibler Stochastic Control
We present two nonparametric approaches to Kullback-Leibler (KL) control, or
linearly-solvable Markov decision problem (LMDP) based on Gaussian processes
(GP) and Nystr\"{o}m approximation. Compared to recently developed parametric
methods, the proposed data-driven frameworks feature accurate function
approximation and efficient on-line operations. Theoretically, we derive the
mathematical connection of KL control based on dynamic programming with earlier
work in control theory which relies on information theoretic dualities for the
infinite time horizon case. Algorithmically, we give explicit optimal control
policies in nonparametric forms, and propose on-line update schemes with
budgeted computational costs. Numerical results demonstrate the effectiveness
and usefulness of the proposed frameworks
Optimal Navigation Functions for Nonlinear Stochastic Systems
This paper presents a new methodology to craft navigation functions for
nonlinear systems with stochastic uncertainty. The method relies on the
transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear
partial differential equation. This approach allows for optimality criteria to
be incorporated into the navigation function, and generalizes several existing
results in navigation functions. It is shown that the HJB and that existing
navigation functions in the literature sit on ends of a spectrum of
optimization problems, upon which tradeoffs may be made in problem complexity.
In particular, it is shown that under certain criteria the optimal navigation
function is related to Laplace's equation, previously used in the literature,
through an exponential transform. Further, analytical solutions to the HJB are
available in simplified domains, yielding guidance towards optimality for
approximation schemes. Examples are used to illustrate the role that noise, and
optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page
Weakly nonlinear stability analysis of MHD channel flow using an efficient numerical approach
We analyze weakly nonlinear stability of a flow of viscous conducting liquid
driven by pressure gradient in the channel between two parallel walls subject
to a transverse magnetic field. Using a non-standard numerical approach, we
compute the linear growth rate correction and the first Landau coefficient,
which in a sufficiently strong magnetic field vary with the Hartmann number as
and
. These
coefficients describe a subcritical transverse velocity perturbation with the
equilibrium amplitude
which exists at Reynolds numbers below the linear stability threshold
We find that the flow
remains subcritically unstable regardless of the magnetic field strength. Our
method for computing Landau coefficients differs from the standard one by the
application of the solvability condition to the discretized rather than
continuous problem. This allows us to bypass both the solution of the adjoint
problem and the subsequent evaluation of the integrals defining the inner
products, which results in a significant simplification of the method.Comment: 16 pages, 10 figures, revised version (to appear in Phys Fluids
Hierarchical Linearly-Solvable Markov Decision Problems
We present a hierarchical reinforcement learning framework that formulates
each task in the hierarchy as a special type of Markov decision process for
which the Bellman equation is linear and has analytical solution. Problems of
this type, called linearly-solvable MDPs (LMDPs) have interesting properties
that can be exploited in a hierarchical setting, such as efficient learning of
the optimal value function or task compositionality. The proposed hierarchical
approach can also be seen as a novel alternative to solving LMDPs with large
state spaces. We derive a hierarchical version of the so-called Z-learning
algorithm that learns different tasks simultaneously and show empirically that
it significantly outperforms the state-of-the-art learning methods in two
classical hierarchical reinforcement learning domains: the taxi domain and an
autonomous guided vehicle task.Comment: 11 pages, 6 figures, 26th International Conference on Automated
Planning and Schedulin
Solving the inverse problem of high numerical aperture focusing using vector Slepian harmonics and vector Slepian multipole fields
A technique using vector Slepian harmonics and multipole fields is presented
for a general treatment of the inverse problem of high numerical aperture
focusing. A prescribed intensity distribution or electric field distribution in
the focal volume is approximated using numerical optimization and the
corresponding illuminating field at the entrance pupil is constructed. Three
examples from the recent literature have been chosen to illustrate the method
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