2,916 research outputs found
Distributed Control by Lagrangian Steepest Descent
Often adaptive, distributed control can be viewed as an iterated game between
independent players. The coupling between the players' mixed strategies,
arising as the system evolves from one instant to the next, is determined by
the system designer. Information theory tells us that the most likely joint
strategy of the players, given a value of the expectation of the overall
control objective function, is the minimizer of a Lagrangian function of the
joint strategy. So the goal of the system designer is to speed evolution of the
joint strategy to that Lagrangian minimizing point, lower the expectated value
of the control objective function, and repeat. Here we elaborate the theory of
algorithms that do this using local descent procedures, and that thereby
achieve efficient, adaptive, distributed control.Comment: 8 page
Distributed-memory large deformation diffeomorphic 3D image registration
We present a parallel distributed-memory algorithm for large deformation
diffeomorphic registration of volumetric images that produces large isochoric
deformations (locally volume preserving). Image registration is a key
technology in medical image analysis. Our algorithm uses a partial differential
equation constrained optimal control formulation. Finding the optimal
deformation map requires the solution of a highly nonlinear problem that
involves pseudo-differential operators, biharmonic operators, and pure
advection operators both forward and back- ward in time. A key issue is the
time to solution, which poses the demand for efficient optimization methods as
well as an effective utilization of high performance computing resources. To
address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov
solver. Our algorithm integrates several components: a spectral discretization
in space, a semi-Lagrangian formulation in time, analytic adjoints, different
regularization functionals (including volume-preserving ones), a spectral
preconditioner, a highly optimized distributed Fast Fourier Transform, and a
cubic interpolation scheme for the semi-Lagrangian time-stepping. We
demonstrate the scalability of our algorithm on images with resolution of up to
on the "Maverick" and "Stampede" systems at the Texas Advanced
Computing Center (TACC). The critical problem in the medical imaging
application domain is strong scaling, that is, solving registration problems of
a moderate size of ---a typical resolution for medical images. We are
able to solve the registration problem for images of this size in less than
five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA;
November 201
On the optimal control of steady fluid structure interaction systems
Fluid-structure interaction (FSI) systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow and are commonly studied in many engineering and biomedical fields. Usually those kind of problems are solved in a direct approach, however it is also interesting to study the inverse problem, where the goal is to find the optimal value of some control parameters, such that the FSI problem solution is close to a desired one. In this work the optimal control problem is formulated with the Lagrange multipliers and adjoint variables formalism. In order to recover the symmetry of the state-adjoint system an auxiliary displacement field is introduced and used to extend the velocity field to the structure domain. As a consequence, the adjoint interface forces are balanced automatically. The optimality system is derived from the first order necessary condition by taking the Fréchet derivatives of the augmented Lagrangian with respect to all the variables involved. The optimal solution is obtained through a gradient-based algorithm applied to the optimality system. In order to support the proposed approach numerical test with distributed control, boundary control and parameter estimation are performed
Optimal boundary geometry in an elasticity problem: a systematic adjoint approach
p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables.
Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654
Instantaneous control of interacting particle systems in the mean-field limit
Controlling large particle systems in collective dynamics by a few agents is
a subject of high practical importance, e.g., in evacuation dynamics. In this
paper we study an instantaneous control approach to steer an interacting
particle system into a certain spatial region by repulsive forces from a few
external agents, which might be interpreted as shepherd dogs leading sheep to
their home. We introduce an appropriate mathematical model and the
corresponding optimization problem. In particular, we are interested in the
interaction of numerous particles, which can be approximated by a mean-field
equation. Due to the high-dimensional phase space this will require a tailored
optimization strategy. The arising control problems are solved using adjoint
information to compute the descent directions. Numerical results on the
microscopic and the macroscopic level indicate the convergence of optimal
controls and optimal states in the mean-field limit,i.e., for an increasing
number of particles.Comment: arXiv admin note: substantial text overlap with arXiv:1610.0132
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