Structure Function, Final States and Angular Ordering at Small x

This talks examines the effect of angular ordering on the small-x evolution of the unintegrated gluon distribution, and discusses the characteristic function for the CCFM equation.Comment: 6 pages, 4 postscript figures, talk presented at the "Madrid Workshop on low x Physics", Miraflores de la Sierra, June 18-21 1997

On Phasor Control for Linear Time Invariant systems

In some control applications, where the reference is sinusoidal, phasor-based strategies can be considered. The main advantage of these approaches is that instead of dealing with oscillating signals, one deals with constant or low-frequency signals. However, to implement this solution, several nonlinearities are included into the control loop. Then, linearization are performed around operating points to design a controller, but with no guaranties of performance. In this work, we present a "large-signal" model for the system. Then, considering ideal measurement of instantaneous amplitude and phase, we establish the correspondence between classical control architecture and a phasor-based one. Hence, we show that a controller can be designed as in a classical architecture and implemented in a phasor-based one with a simple transformation, ensuring the same performance level. However, in practical applications, the measurements of amplitude and phase are not ideal and may quickly degrade the behavior of the system. Thus, we propose a second design approach that takes these nonlinearities into account, ensuring nominal stability and performance. Examples illustrate the effectiveness of these methods

Reduced Complexity Controllers for LPV Systems: Towards Incremental Synthesis

International audienceExisting synthesis methods for LPV systems often result in controllers of high complexity. So far, there is no efficient and systematic remedy to this issue as there exists no convex formulation of the problem of finding a solution of reduced complexity to the general case LPV synthesis problem. In this paper, the specific case is considered when parameter-dependent signals are measured. It is proven that these measures can be exploited so that the problem of reduced-complexity controller synthesis can be written as an LMI optimization problem. A complete procedure for the controller construction is provided. The interest of the result is discussed in relation with nonlinear methods. First, an interpretation of the controller strategy is proposed with regard to the feedback linearization method. Second, it is proven that a nonlinear controller ensuring the closed loop incremental properties can be constructed

H∞ loop shaping control for distributed PLL network

International audienceIn this paper, we describe a robust control law for distributed PLL network using H∞ optimization problem. The controller can be uniformly applied on all distributed nodes and guarantees good stability margins, enhanced performance and reduced jitter noise. A 2-dimensional Cartesian mesh network structure is considered without using any feedback loop phase information propagation to eliminate undesirable mode-locked states

Approche de la performance relative pour la commande de systèmes de grande dimension

International audienceDans ce papier, le problème de la synthèse de la loi de commande décentralisée pour des systèmes de grande dimension ou des systèmes de Multi-Agents composés de sous-systèmes identiques, assurant la stabilité et un niveau de performance globales, est considéré. Inspiré par l'approche entrée-sortie, le problème de synthèse est réduit à un problème de satisfaction de deux contraintes : (i) la contrainte sur la dynamique du système d'interconnexion et (ii) la contrainte sur la dynamique des sous-systèmes locaux (ou agents). Les deux problèmes ont été résolus en appliquant l'optimisation convexe sous contraintes LMI et une synthèse H ∞ standard. La méthode proposée est appliquée à la synthèse de la loi de commande pour la synchronisation du réseau de PLLs

Control Law Design for Distributed Multi-Agent Systems

In this paper, the problem of control law design for decentralized homogenous Multi-Agent systems ensuring the global stability and global performance properties is considered. Inspired by the decentralized control law design methodology using the dissipativity input-output approach, the problem is reduced to the problem of satisfying two conditions: (i) the condition on the interconnection and (ii) the condition on the local agent dynamics. Both problems are e fficiently solved applying a (quasi-) convex optimization under Linear Matrix Inequality (LMI) constraints and an H infinity synthesis. The proposed design methodology is applied to the control law design of a synchronous PLLs network

Network Internal Signal Feedback and Injection: Interconnection Matrix Design

International audienceThe design of systems defined as networks (interconnections) of identical subsystems emerges as an interesting engineering problem, with some open issues. One of these issuesis how to "retune" the interconnection in order to ensure the stability and the performance of the system. Based on the LFT representation and on the input-output framework, we propose in this paper some efficient "retuning" methods using convex optimization involving LMI constraints. The proposed approach can be interpreted as an extension of usual state space methods. Its application is investigated for the design of a network of PLLs

Small-x one-particle-inclusive quantities in the CCFM approach

This article presents the results of a quantitative study of the small-x data at HERA, using the CCFM equation. The first step consists of choosing the version of the CCFM equation to be used, corresponding to selecting a particular subset of next-to-leading-logarithmic corrections --- the choice is constrained by requiring a phenomenologically reasonable small-x growth. For the time being, the parts of the splitting functions that are finite at z=0 have been left out. We then examine results for F_2^c, R, the transverse energy flow, the charged-particle transverse-momentum spectrum and the forward-jet cross section and compare to data. While some of the data is reproduced better than with DGLAP-based calculations, the agreement is not entirely satisfactory, suggesting that the approach developed here is not yet suitable for detailed phenomenology. We discuss why, and suggest directions for future work.Comment: 33 pages, 10 figures, uses cite.sty and JHEP.cls (both included). Version 2 includes additional and updated reference

Performance Control for Interconnection of Identical Systems: Application to PLL network design

International audienceIn this paper, the problem of the control law design for interconnected identical systems ensuring the global stability and the global performance properties is under consideration. Inspired by the decentralized control law design methodology using the dissipativity input–output approach, the problem is reduced to the problem of satisfying two conditions: (i) the condition on the interconnection and (ii) the condition on the local subsystem dynamics. Both problems are efficiently solved applying a (quasi‐) convex LMI optimization and standard H∞ synthesis. The proposed design methodology is applied to the control law design of a synchronous PLL network