Decentralized estimators for a large scale dynamic system

In this paper, we propose an extended block Krylov process to construct two biorthogonal bases for the extended Krylov subspaces \(\mathbb {K}_{m}^e(A,V)\) and \(\mathbb {K}_{m}^e(A^{T},W)\), where \(A \in \mathbb {R}^{n \times n}\) and \(V,~W \in \mathbb {R}^{n \times p}\). After deriving some new theoretical results and algebraic properties, we apply the proposed algorithm with moment matching techniques for model reduction in large scale dynamical systems. Numerical experiments for large and sparse problems are given to show the efficiency of the proposed method.

Hybrid decentralized maximum entropy control for large-scale dynamical systems

Event dissemination in large scale dynamic systems is typically claimed to be best achieved using decentralized peer-to-peer architectures. The rationale is to have every participant in the system act both as a client (information consumer) and as a server (information dissemination enabler), thus, precluding specific brokers which would prevent scalability and fault-tolerance. We argue that, for such decentralized architectures to be really meaningful, participants should serve the system as much as they benefit from it. That is, the system should be fair in the sense that the extend to which a participant acts as a server should depend on the extend to which it has the opportunity to act as a client. This is particularly crucial in selective information dissemination schemes where clients are not all interested in the same information. In this position paper, we discuss what a notion of fairness could look like, explain why current architectures are not fair, and raise several challenges towards achieving fairness.

124 Resource allocation in large scale dynamic system with different information of controllers

On the probability of chaos in large dynamical systems: A Monte Carlo study

Peer-to-peer (P2P) computing has become a popular distributed computing paradigm thanks to abundant computing power of modern desktop workstations and widely available network connectivity via the Internet. Although P2P file sharing provides a scalable alternative to conventional server-based approaches, providing efficient file search in a large scale dynamic P2P system remains a challenging problem. In this paper, we propose a set of mechanisms to provide a scalable keyword-based file search in distributed hash table (DHT)-based P2P systems. In particular, we address the problem induced by common keywords that are associated with a large number of files and thus require excessive storage consumptions from the hosting peers. Our proposed architecture, called keyword fusion, adaptively unburdens the peers overloaded with excessive storage consumptions due to common keywords and reduces network bandwidth consumption by transforming users' queries to contain more focused search terms. Through trace-driven simulations, we show that keyword fusion can reduces the storage consumption of the top 5% most loaded nodes by 50% and decrease the search traffic by up to 68% even in the modest scenarios of combining two keywords.

Understanding the relationship between complexity and stability in large dynamical systems—such as ecosystems—remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of ‘stability’ in fact has other uses in the empirical ecological literature. The important notion of ‘temporal stability’ describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis of ecological time-series data of plankton abundances.

In this paper, we study the (h/sub 0/, h)-practical stability of large scale dynamic system with impulsive solution. By using comparison principle, scalar and vector Lyapunov functions and impulsive different inequalities, we obtain some sufficient conditions of the (h/sub 0/, h)-practical stability for large scale impulsive dynamic system in terms of two measurements.

Significant research efforts have been devoted to large-scale dynamical systems, with the aim of understanding their complicated behaviors and managing their responses in real-time. One pivotal technological obstacle in this process is the existence of uncertainty. Although many of these large-scale dynamical systems function well in the design stage, they may easily fail when operating in realistic environment, where environmental uncertainties modulate system dynamics and complicate real-time predication and management tasks. This dissertation aims to develop systematic methodologies to evaluate the performance of large-scale dynamical systems under uncertainty, as a step toward real-time decision support. Two uncertainty evaluation approaches are pursued: the analytical approach and the effective simulation approach. The analytical approach abstracts the dynamics of original stochastic systems, and develops tractable analysis (e.g., jump-linear analysis) for the approximated systems. Despite the potential bias introduced in the approximation process, the analytical approach provides rich insights valuable for evaluating and managing the performance of large-scale dynamical systems under uncertainty. When a system’s complexity and scale are beyond tractable analysis, the effective simulation approach becomes very useful. The effective simulation approach aims to use a few smartly selected simulations to quickly evaluate a complex system’s statistical performance. This approach was originally developed to evaluate a single uncertain variable. This dissertation extends the approach to be scalable and effective for evaluating large-scale systems under a large-number of uncertain variables. While a large portion of this dissertation focuses on the development of generic methods and theoretical analysis that are applicable to broad large-scale dynamical systems, many results are illustrated through a representative large-scale system application on strategic air traffic management application, which is concerned with designing robust management plans subject to a wide range of weather possibilities at 2-15 hours look-ahead time.

Lyapunov modal analysis and participation factors applied to small-signal stability of power systems

We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such dynamical systems: First, infinitely large systems on directed graphs can be stable even when the degree distribution has unbounded support; this result is surprising since their counterparts on nondirected graphs are unstable when system size is large enough. Second, we show that the phase transition between the stable and unstable phase is universal in the sense that it depends only on a few parameters, such as, the mean degree and a degree correlation coefficient. In addition, in the unstable regime we characterize the nature of the destabilizing mode, which also exhibits universal features. These results follow from an exact theory for the leading eigenvalue of infinitely large graphs that are locally tree-like and oriented, as well as, for the right and left eigenvectors associated with the leading eigenvalue. We corroborate analytical results for infinitely large graphs with numerical experiments on random graphs of finite size. We discuss how the presented theory can be extended to graphs with diagonal disorder and to graphs that contain nondirected links. Finally, we discuss the influence of small cycles and how they can destabilize large dynamical systems when they induce strong enough feedback loops.

We discuss the stabilization of large scale linear time invariant dynamical systems via feedback. An overview of efficient schemes based on the discrete Riccati difference equation are presented. In particular, results are given for a Newton-like approach to the problem.

Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems is based on the combined proceedings of two workshops devoted to computational issues. The workshops were an integral part of the 1997-98 IMA program on EMERGING APPLICATIONS OF DYNAMICAL SYSTEMS. I would like to thank Donald G. Aronson, University of Minnesota (Mathematics); Wolf-Juergen Beyn, Universitaet Bielefeld (Fakultaet fuer Mathematik); Eusebius Doedel, California Institute of Technology (Applied Mathematics); Bernold Fiedler, Free University of Berlin (Mathematics); H.B. Keller, Caltech (Applied Mathematics); Yannis Kevrekidis, Princeton University (Chemical Enginering); Jens Lorenz, University of New Mexico (Mathematics and Statistics); Edriss S. Titi, University of California (Mathematics); Laurette S. Tuckerman, Laboratoire d'Informatique pour la Mecanique et les Sciences de l'Ingenieur (LIMSI) for their excellent work as organizers of the meeting. Special appreciation to Eusebius Doedel and Laurette S. Tuckerman for serving as editors of the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the National Security Agency (NSA), whose financial support made the workshop possible.

This paper presents an adaptive filter for real-time calibration of redundant signals consisting of sensor data and/or analytically derived measurements. The measurement noise covariance matrix is adjusted as a function of the a posteriori probabilities of failure of the individual signals. An estimate of the measured variable is obtained as a weighted average of the calibrated signals. The weighting matrix is recursively updated in real time instead of being fixed a priori. The filter software is presently hosted in a Pentium platform and is portable to other commercial platforms. The filter can be used to enhance the Instrumentation and Control System Software in large-scale dynamical systems.

It is important content that the studying connective stability among the stability studying of the large-scale interconnected systems. The many results recently have been given for the normal systems, the studying result of the singular large scale systems, however, is a little. The paper discussed the connective stability of a kind of nonlinear singular large-scale dynamical systems by means of singular Lyapunov equation and vector Lyapunov function. A stable domain of connective parameters is given in the paper which is simple in form. At last we give an example to show the usage of the method and its efficiency.