An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems

Principal component analysis is used to decompose a large scale dynamic system into robust subsystems. Decentralized state estimators are then designed to observe the states of the individual subsystems. The estimators are useful in the identification of states which are strongly controllable and/or strongly observable in the inputs and outputs, respectively. The decentralized estimators have few elements and are easy to implement and tune in real time. The decentralized estimators were verified by simulation. Simulation results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

Dimensionally reduced Krylov subspace model reduction for large scale systems

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

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.

In this paper, we present a structure-preserving model-order reduction method for solving large-scale second-order MIMO dynamical systems. It is a projection method based on a block second-order Krylov subspace. We use the block second-order Arnoldi (BSOAR) method to generate an orthonormal basis of the projection subspace. The reduced system preserves the second-order structure of the original system. Some theoretical results are given. Numerical experiments report the effectiveness of this method.

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.

Two-sided projection methods are presented for model reduction of large scale multi-input multi-output bilinear systems. By properly choosing projection matrices, the reduced model possesses a superior moment matching property and we prove it from a new perspective by means of linear equations. The preservation of stability for reduced models is also considered. In contrast to the most existing approaches, we construct the reduced model directly instead of using an iterative procedure, thereby saving much computational cost. As two-sided methods are more likely to produce badly ill-conditioned system matrices, a mixed algorithm having the benefits of one-sided and two-sided methods is proposed at the cost of roughly doubling the dimension of reduced models. Theoretical analysis and numerical experiments show the efficiency of our approach.

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.

A new method for model reduction and controller design of large-scale dynamical systems

Reduced Order Controller Design for Discrete Time Systems