130 research outputs found
Preconditioned warm-started Newton-Krylov methods for MPC with discontinuous control
We present Newton-Krylov methods for efficient numerical solution of optimal
control problems arising in model predictive control, where the optimal control
is discontinuous. As in our earlier work, preconditioned GMRES practically
results in an optimal complexity, where is a discrete horizon
length. Effects of a warm-start, shifting along the predictive horizon, are
numerically investigated. The~method is tested on a classical double integrator
example of a minimum-time problem with a known bang-bang optimal control.Comment: 8 pages, 10 figures, to appear in Proceedings SIAM Conference on
Control and Its Applications, July 10-12, 2017, Pittsburgh, PA, US
Sparse preconditioning for model predictive control
We propose fast O(N) preconditioning, where N is the number of gridpoints on
the prediction horizon, for iterative solution of (non)-linear systems
appearing in model predictive control methods such as forward-difference
Newton-Krylov methods. The Continuation/GMRES method for nonlinear model
predictive control, suggested by T. Ohtsuka in 2004, is a specific application
of the Newton-Krylov method, which uses the GMRES iterative algorithm to solve
a forward difference approximation of the optimality equations on every time
step.Comment: 6 pages, 5 figures, to appear in proceedings of the American Control
Conference 2016, July 6-8, Boston, MA, USA. arXiv admin note: text overlap
with arXiv:1509.0286
Accelerated graph-based nonlinear denoising filters
Denoising filters, such as bilateral, guided, and total variation filters,
applied to images on general graphs may require repeated application if noise
is not small enough. We formulate two acceleration techniques of the resulted
iterations: conjugate gradient method and Nesterov's acceleration. We
numerically show efficiency of the accelerated nonlinear filters for image
denoising and demonstrate 2-12 times speed-up, i.e., the acceleration
techniques reduce the number of iterations required to reach a given peak
signal-to-noise ratio (PSNR) by the above indicated factor of 2-12.Comment: 10 pages, 6 figures, to appear in Procedia Computer Science, vol.80,
2016, International Conference on Computational Science, San Diego, CA, USA,
June 6-8, 201
Signal reconstruction via operator guiding
Signal reconstruction from a sample using an orthogonal projector onto a
guiding subspace is theoretically well justified, but may be difficult to
practically implement. We propose more general guiding operators, which
increase signal components in the guiding subspace relative to those in a
complementary subspace, e.g., iterative low-pass edge-preserving filters for
super-resolution of images. Two examples of super-resolution illustrate our
technology: a no-flash RGB photo guided using a high resolution flash RGB
photo, and a depth image guided using a high resolution RGB photo.Comment: 5 pages, 8 figures. To appear in Proceedings of SampTA 2017: Sampling
Theory and Applications, 12th International Conference, July 3-7, 2017,
Tallinn, Estoni
Accelerated graph-based spectral polynomial filters
Graph-based spectral denoising is a low-pass filtering using the
eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial
filtering avoids costly computation of the eigendecomposition by projections
onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the
bilateral and guided filters. We propose constructing accelerated polynomial
filters by running flexible Krylov subspace based linear and eigenvalue solvers
such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG)
method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop
on Machine Learning for Signal Processin
Preconditioned Continuation Model Predictive Control
Model predictive control (MPC) anticipates future events to take appropriate
control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models
and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T.
Ohtsuka in 2004, uses the GMRES iterative algorithm to solve a forward
difference approximation of the Continuation NMPC (CNMPC) equations on
every time step. The coefficient matrix of the linear system is often
ill-conditioned, resulting in poor GMRES convergence, slowing down the on-line
computation of the control by CNMPC, and reducing control quality. We adopt
CNMPC for challenging minimum-time problems, and improve performance by
introducing efficient preconditioning, utilizing parallel computing, and
substituting MINRES for GMRES.Comment: 8 pages, 6 figures. To appear in Proceedings SIAM Conference on
Control and Its Applications, July 8-10, 2015, Paris, Franc
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