A Global Steering Method for Nonholonomic Systems

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in [29] for chained-form systems

Sampling-based learning control of inhomogeneous quantum ensembles

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\Lambda$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find the control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented showing the success of the SLC method.Comment: 8 pages, 9 figure

Time minimal trajectories for two-level quantum systems with two bounded controls

In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we tackle the time-optimal control problem with techniques of optimal synthesis on 2-D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the starting point

Searching for quantum optimal controls under severe constraints

The success of quantum optimal control for both experimental and theoretical objectives is connected to the topology of the corresponding control landscapes, which are free from local traps if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is of full rank, and (3) there are no constraints on the control field. This paper investigates how the violation of assumption (3) affects gradient searches for globally optimal control fields. The satisfaction of assumptions (1) and (2) ensures that the control landscape lacks fundamental traps, but certain control constraints can still introduce artificial traps. Proper management of these constraints is an issue of great practical importance for numerical simulations as well as optimization in the laboratory. Using optimal control simulations, we show that constraints on quantities such as the number of control variables, the control duration, and the field strength are potentially severe enough to prevent successful optimization of the objective. For each such constraint, we show that exceeding quantifiable limits can prevent gradient searches from reaching a globally optimal solution. These results demonstrate that careful choice of relevant control parameters helps to eliminate artificial traps and facilitate successful optimization.Comment: 16 pages, 7 figure

Interactions of the apolipoprotein C-III 3238C>G polymorphism and alcohol consumption on serum triglyceride levels

<p>Abstract</p> <p>Background</p> <p>Both apolipoprotein (Apo) C-III gene polymorphism and alcohol consumption have been associated with increased serum triglyceride (TG) levels, but their interactions on serum TG levels are not well known. The present study was undertaken to detect the interactions of the ApoC-III 3238C>G (rs5128) polymorphism and alcohol consumption on serum TG levels.</p> <p>Methods</p> <p>A total of 516 unrelated nondrinkers and 514 drinkers aged 15-89 were randomly selected from our previous stratified randomized cluster samples. Genotyping of the ApoC-III 3238C>G was performed by polymerase chain reaction and restriction fragment length polymorphism combined with gel electrophoresis, and then confirmed by direct sequencing. Interactions of the ApoC-III 3238C>G genotype and alcohol consumption was assessed by using a cross-product term between genotypes and the aforementioned factor.</p> <p>Results</p> <p>Serum total cholesterol (TC), TG, high-density lipoprotein cholesterol (HDL-C), ApoA-I and ApoB levels were higher in drinkers than in nondrinkers (<it>P </it>< 0.05-0.001). There was no significant difference in the genotypic and allelic frequencies between the two groups. Serum TG levels in nondrinkers were higher in CG genotype than in CC genotype (<it>P </it>< 0.01). Serum TC, TG, low-density lipoprotein cholesterol (LDL-C) and ApoB levels in drinkers were higher in GG genotype than in CC or CG genotype (<it>P </it>< 0.01 for all). Serum HDL-C levels in drinkers were higher in CG genotype than in CC genotype (<it>P </it>< 0.01). Serum TC, TG, HDL-C and ApoA-I levels in CC genotype, TC, HDL-C, ApoA-I levels and the ratio of ApoA-I to ApoB in CG genotype, and TC, TG, LDL-C, ApoA-I and ApoB levels in GG genotype were higher in drinkers than in nondrinkers (<it>P </it>< 0.05-0.01). But the ratio of ApoA-I to ApoB in GG genotype was lower in drinkers than in nondrinkers (<it>P </it>< 0.01). Multivariate logistic regression analysis showed that the levels of TC, TG and ApoB were correlated with genotype in nondrinkers (<it>P </it>< 0.05 for all). The levels of TC, LDL-C and ApoB were associated with genotype in drinkers (<it>P </it>< 0.01 for all). Serum lipid parameters were also correlated with age, sex, alcohol consumption, cigarette smoking, blood pressure, body weight, and body mass index in both groups.</p> <p>Conclusions</p> <p>This study suggests that the ApoC-III 3238CG heterozygotes benefited more from alcohol consumption than CC and GG homozygotes in increasing serum levels of HDL-C, ApoA-I, and the ratio of ApoA-I to ApoB, and lowering serum levels of TC and TG.</p

Planification de mouvements pour les systèmes non-holonomes et étude de la contrôlabilité spectrale pour les équations de Schrödinger linéarisées

Abstract : The objective of this thesis is, firstly, to provide motion planning algorithms for nonholonomic systems, and secondly, to study the spectral controllability for the linearized Schrödinger equations. We made a double contribution to the problem of motion planning for nonholonomic systems. Based on the sub- Riemannian geometry , we have developed a new algorithm that completely solves the problem in a general framework. We have also proposed a numerical implementation of the continuation method that provides satisfactory solutions to the rollingbody problem, a classic example of nonholonomic systems with two inputs. We have given necessary and sufficient conditions of spectral controllability in finite time for the linearized Schrödinger equations in dimension 2 and 3. Their genericity with respect to the domain has been studied by a novel technique based on integral equations.L'objectif de cette thèse est, d'une part, de fournir des méthodes de planification de mouvements pour les systèmes non-holonomes, et d'autre part, d'étudier la contrôlabilité spectrale pour les équations de Schrödinger linéarisées. Nous avons apporté une double contribution au problème de la planification de mouvements pour les systèmes non-holonomes. Fondé sur la géométrie sous-riemannienne, nous avons conçu un nouvel algorithme qui résout complètement le problème dans un cadre général. Nous avons également proposé une implémentation numérique de la méthode de continuation qui fournit des solutions satisfaisantes au problème de la planification du roulement sur le plan, un exemple classique de systèmes non-holonomes à deux entrées. Nous avons donné des conditions nécessaires et suffisantes de contrôlabilité spectrale en temps fini des équations de Schrödinger linéarisées en dimension 2 et 3. Leur généricité par rapport au domaine a été étudiée par une technique originale basée sur les équations intégrales