22,267 research outputs found
A search algorithm for a class of optimal finite-precision controller realization problems with saddle points
With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them
An improved closed-loop stability related measure for finite-precision digital controller realizations
The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller, implemented with finite word length (FWL), is used. A new stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure
An improved closed-loop stability related measure for finite-precision digital controller realizations
The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller, implemented with finite word length (FWL), is used. A new stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure
Shape restricted regression with random Bernstein polynomials
Shape restricted regressions, including isotonic regression and concave
regression as special cases, are studied using priors on Bernstein polynomials
and Markov chain Monte Carlo methods. These priors have large supports, select
only smooth functions, can easily incorporate geometric information into the
prior, and can be generated without computational difficulty. Algorithms
generating priors and posteriors are proposed, and simulation studies are
conducted to illustrate the performance of this approach. Comparisons with the
density-regression method of Dette et al. (2006) are included.Comment: Published at http://dx.doi.org/10.1214/074921707000000157 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing Transform
This study introduces a new adaptive time-frequency (TF) analysis technique,
synchrosqueezing transform (SST), to explore the dynamics of a laser-driven
hydrogen atom at an {\it ab initio} level, upon which we have demonstrated its
versatility as a new viable venue for further exploring quantum dynamics. For a
signal composed of oscillatory components which can be characterized by
instantaneous frequency, the SST enables rendering the decomposed signal based
on the phase information inherited in the linear TF representation with
mathematical support. Compared with the classical type TF methods, the SST
clearly depicts several intrinsic quantum dynamical processes such as selection
rules, AC Stark effects, and high harmonic generation
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