14,948 research outputs found
An Extended Kalman Filter for Data-enabled Predictive Control
The literature dealing with data-driven analysis and control problems has
significantly grown in the recent years. Most of the recent literature deals
with linear time-invariant systems in which the uncertainty (if any) is assumed
to be deterministic and bounded; relatively little attention has been devoted
to stochastic linear time-invariant systems. As a first step in this direction,
we propose to equip the recently introduced Data-enabled Predictive Control
algorithm with a data-based Extended Kalman Filter to make use of additional
available input-output data for reducing the effect of noise, without
increasing the computational load of the optimization procedure
Ergodic Randomized Algorithms and Dynamics over Networks
Algorithms and dynamics over networks often involve randomization, and
randomization may result in oscillating dynamics which fail to converge in a
deterministic sense. In this paper, we observe this undesired feature in three
applications, in which the dynamics is the randomized asynchronous counterpart
of a well-behaved synchronous one. These three applications are network
localization, PageRank computation, and opinion dynamics. Motivated by their
formal similarity, we show the following general fact, under the assumptions of
independence across time and linearities of the updates: if the expected
dynamics is stable and converges to the same limit of the original synchronous
dynamics, then the oscillations are ergodic and the desired limit can be
locally recovered via time-averaging.Comment: 11 pages; submitted for publication. revised version with fixed
technical flaw and updated reference
A Neuroevolutionary Approach to Stochastic Inventory Control in Multi-Echelon Systems
Stochastic inventory control in multi-echelon systems poses hard problems in optimisation under uncertainty. Stochastic programming can solve small instances optimally, and approximately solve larger instances via scenario reduction techniques, but it cannot handle arbitrary nonlinear constraints or other non-standard features. Simulation optimisation is an alternative approach that has recently been applied to such problems, using policies that require only a few decision variables to be determined. However, to find optimal or near-optimal solutions we must consider exponentially large scenario trees with a corresponding number of decision variables. We propose instead a neuroevolutionary approach: using an artificial neural network to compactly represent the scenario tree, and training the network by a simulation-based evolutionary algorithm. We show experimentally that this method can quickly find high-quality plans using networks of a very simple form
A convergent relaxation of the Douglas-Rachford algorithm
This paper proposes an algorithm for solving structured optimization
problems, which covers both the backward-backward and the Douglas-Rachford
algorithms as special cases, and analyzes its convergence. The set of fixed
points of the algorithm is characterized in several cases. Convergence criteria
of the algorithm in terms of general fixed point operators are established.
When applying to nonconvex feasibility including the inconsistent case, we
prove local linear convergence results under mild assumptions on regularity of
individual sets and of the collection of sets which need not intersect. In this
special case, we refine known linear convergence criteria for the
Douglas-Rachford algorithm (DR). As a consequence, for feasibility with one of
the sets being affine, we establish criteria for linear and sublinear
convergence of convex combinations of the alternating projection and the DR
methods. These results seem to be new. We also demonstrate the seemingly
improved numerical performance of this algorithm compared to the RAAR algorithm
for both consistent and inconsistent sparse feasibility problems
Quantum systems and control 1
http://www-direction.inria.fr/international/arima/009/00920.htmlInternational audienceThis paper describes several methods used by physicists for manipulations of quantum states. For each method, we explain the model, the various time-scales, the performed approximations and we propose an interpretation in terms of control theory. These various interpretations underlie open questions on controllability, feedback and estimations. For 2-level systems we consider: the Rabi oscillations in connection with averaging; the Bloch-Siegert corrections associated to the second order terms; controllability versus parametric robustness of open-loop control and an interesting controllability problem in infinite dimension with continuous spectra. For 3-level systems we consider: Raman pulses and the second order terms. For spin/spring systems we consider: composite systems made of 2-level sub-systems coupled to quantized harmonic oscillators; multi-frequency averaging in infinite dimension; controllability of 1D partial differential equation of Shrödinger type and affine versus the control; motion planning for quantum gates. For open quantum systems subject to decoherence with continuous measures we consider: quantum trajectories and jump processes for a 2-level system; Lindblad-Kossakovsky equation and their controllability.Ce papier décrit plusieurs méthodes utilisées par les physiciens pour la manipulation d’états quantiques. Pour chaque méthode, nous expliquons la modélisation, les diverses échelles de temps, les approximations faites et nous proposons une interprétation en termes de contrôle. Ces diverses interprétations servent de base à la formulation de questions ouvertes sur la commandabilité et aussi sur le feedback et l’estimation, renouvelant un peu certaines questions de base en théorie des systèmes non-linéaires. Pour les systèmes à deux niveaux, dits aussi de spin 1/2, il s’agit: des oscillations de Rabi et d’une approximation au premier ordre de la théorie des perturbations (transition à un photon); des corrections de Bloch-Siegert et d’approximation au second ordre; de commandabilité et de robustesse paramétrique pour des contrôles en boucle ouverte, robustesse liée à des questions largement ouvertes sur la commandabilité en dimension infinie où le spectre est continu. Pour les systèmes à trois niveaux, il s’agit: de pulses Raman; d’approximations au second ordre. Pour les systèmes spin/ressort, il s’agit: des systèmes composés de sous-systèmes à deux niveaux couplés à des oscillateurs harmoniques quantifiés; de théorie des perturbations à plusieurs fréquences en dimension infinie; de commandabilité d’équations aux dérivées partielles de type Schrödinger sur R et affine en contrôle; de planification de trajectoires pour la synthèse portes logiques quantiques. Pour les systèmes ouverts soumis à la décohérence avec des mesures en continu, il s’agit: de trajectoires quantiques de Monte-Carlo et de processus à sauts sur un systèmes à deux niveaux; des équations de Lindblad-Kossakovsky avec leur commandabilité
Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
We have studied how 2- and 3- dimensional systems made up of particles
interacting with finite range, repulsive potentials jam (i.e., develop a yield
stress in a disordered state) at zero temperature and applied stress. For each
configuration, there is a unique jamming threshold, , at which
particles can no longer avoid each other and the bulk and shear moduli
simultaneously become non-zero. The distribution of values becomes
narrower as the system size increases, so that essentially all configurations
jam at the same in the thermodynamic limit. This packing fraction
corresponds to the previously measured value for random close-packing. In fact,
our results provide a well-defined meaning for "random close-packing" in terms
of the fraction of all phase space with inherent structures that jam. The
jamming threshold, Point J, occurring at zero temperature and applied stress
and at the random close-packing density, has properties reminiscent of an
ordinary critical point. As Point J is approached from higher packing
fractions, power-law scaling is found for many quantities. Moreover, near Point
J, certain quantities no longer self-average, suggesting the existence of a
length scale that diverges at J. However, Point J also differs from an ordinary
critical point: the scaling exponents do not depend on dimension but do depend
on the interparticle potential. Finally, as Point J is approached from high
packing fractions, the density of vibrational states develops a large excess of
low-frequency modes. All of these results suggest that Point J may control
behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure
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