26,545 research outputs found
An Overview of Variational Integrators
The purpose of this paper is to survey some recent advances in variational
integrators for both finite dimensional mechanical systems as well as continuum
mechanics. These advances include the general development of discrete
mechanics, applications to dissipative systems, collisions, spacetime integration algorithms,
AVI’s (Asynchronous Variational Integrators), as well as reduction for
discrete mechanical systems. To keep the article within the set limits, we will only
treat each topic briefly and will not attempt to develop any particular topic in
any depth. We hope, nonetheless, that this paper serves as a useful guide to the
literature as well as to future directions and open problems in the subject
Distributed Receding Horizon Control with Application to Multi-Vehicle Formation Stabilization
We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen sufficiently fast. The theory is applied in simulation for stabilization of a formation of vehicles
Frequency-Weighted Model Reduction with Applications to Structured Models
In this paper, a frequency-weighted extension of a
recently proposed model reduction method for linear systems
is presented. The method uses convex optimization and can be
used both with sample data and exact models. We also obtain
bounds on the frequency-weighted error. The method is combined
with a rank-minimization heuristic to approximate multiinput–
multi-output systems.We also present two applications—
environment compensation and simplification of interconnected
models — where we argue the proposed methods are useful
Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM
We present the implementation of a three-dimensional, second order accurate
Godunov-type algorithm for magneto-hydrodynamic (MHD), in the
adaptive-mesh-refinement (AMR) cosmological code {\tt CHARM}. The algorithm is
based on the full 12-solve spatially unsplit Corner-Transport-Upwind (CTU)
scheme. The fluid quantities are cell-centered and are updated using the
Piecewise-Parabolic-Method (PPM), while the magnetic field variables are
face-centered and are evolved through application of the Stokes theorem on cell
edges via a Constrained-Transport (CT) method. The multidimensional MHD source
terms required in the predictor step for high-order accuracy are applied in a
simplified form which reduces their complexity in three dimensions without loss
of accuracy or robustness. The algorithm is implemented on an AMR framework
which requires specific synchronization steps across refinement levels. These
include face-centered restriction and prolongation operations and a {\it
reflux-curl} operation, which maintains a solenoidal magnetic field across
refinement boundaries. The code is tested against a large suite of test
problems, including convergence tests in smooth flows, shock-tube tests,
classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud
interaction problem and the formation of a cluster of galaxies in a fully
cosmological context. The magnetic field divergence is shown to remain
negligible throughout.Comment: 53 pages, 17 figs, under review by ApJ
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