Distributed Signal Processing over Large-Scale Complex Systems

Large-scale and complex dynamical networks with high-dimension states have been emerging in the era of big data, which potentially generate massive data sets. To deal with the massive data sets, one promising method is the distributed collaboration strategy over the network. This dissertation proposes the schemes of distributed estimation and distributed quickest detection and also studies the performance of the distributed schemes with the large deviation analysis, which answers a fundamental question on how to quantify the rate at which the distributed scheme approaches the centralized performance. First, the distributed Kalman filtering scheme with the Gossip interaction among sensors is proposed to estimate the high-dimension states at each node, where sensors exchange their filtered states (estimates and error covariance) and propagate their observations via inter-sensor communications. The conditional estimation error covariance sequence at each sensor under this scheme is proven to evolve as a random Riccati equation (RRE) with Markov modulated switching. By formulating the RRE as a random dynamical system, it is shown that the network consensus over the estimation at each node is achieved. The large deviation analysis further shows that the distributed scheme converges to the optimal centralized one at an exponentially fast rate. By considering the energy and bandwidth constrains, a Quantized Gossip-based Interactive Kalman Filtering algorithm for scalar dynamic systems is also proposed, where the sensors exchange their quantized states with neighbors via inter-sensor communications. It is shown that, in the countable infinite quantization alphabet case, the network can still achieve weak consensus with the additional information loss caused by quantization. It is also proved that, under certain conditions, the network can also achieve weak consensus with the finite quantization alphabet, which is more restricted and practical. Then, the distributed quickest detection scheme is proposed with multiple rounds of inter-sensor communications to propagate observations during the sampling interval. By modeling the information propagation dynamics in the network as a Markov process, the two-layer large deviation analysis is used to analyze the performance of the distributed scheme. The first layer analysis proves that the probability of false alarm decays to zero exponentially fast with the increasing of the averaged detection delay, where the Kullback-Leibler (KL) information number is established as a crucial factor. The second-layer analysis shows that the probability of the rare event that not all observations are available at a sensor decays to zero at an exponentially fast rate when the number of communications increases, where the large deviation upper and lower bounds for this rate are also derived, based on which it is shown that the performance of the distributed algorithm converges exponentially fast to that of the centralized one, by proving that the defined distributed KL information number converges to the centralized KL information number

Large-scale Complex IT Systems

This paper explores the issues around the construction of large-scale complex systems which are built as 'systems of systems' and suggests that there are fundamental reasons, derived from the inherent complexity in these systems, why our current software engineering methods and techniques cannot be scaled up to cope with the engineering challenges of constructing such systems. It then goes on to propose a research and education agenda for software engineering that identifies the major challenges and issues in the development of large-scale complex, software-intensive systems. Central to this is the notion that we cannot separate software from the socio-technical environment in which it is used.Comment: 12 pages, 2 figure

Qualitative Fault Detection and Hazard Analysis Based on Signed Directed Graphs for Large-Scale Complex Systems

Nowadays in modern industries, the scale and complexity of process systems are increased continuously. These systems are subject to low productivity, system faults or even hazards because of various conditions such as mis-operation, equipment quality change, externa

Extremal Properties of Three Dimensional Sensor Networks with Applications

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that $n$ nodes, each capable of sensing events within a radius of $r$, are randomly and uniformly distributed in a 3-dimensional region $\mathcal{R}$ of volume $V$, how large must the sensing range be to ensure a given degree of coverage of the region to monitor? For a given transmission range, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations

Modes of Information Flow

Information flow between components of a system takes many forms and is key to understanding the organization and functioning of large-scale, complex systems. We demonstrate three modalities of information flow from time series X to time series Y. Intrinsic information flow exists when the past of X is individually predictive of the present of Y, independent of Y's past; this is most commonly considered information flow. Shared information flow exists when X's past is predictive of Y's present in the same manner as Y's past; this occurs due to synchronization or common driving, for example. Finally, synergistic information flow occurs when neither X's nor Y's pasts are predictive of Y's present on their own, but taken together they are. The two most broadly-employed information-theoretic methods of quantifying information flow---time-delayed mutual information and transfer entropy---are both sensitive to a pair of these modalities: time-delayed mutual information to both intrinsic and shared flow, and transfer entropy to both intrinsic and synergistic flow. To quantify each mode individually we introduce our cryptographic flow ansatz, positing that intrinsic flow is synonymous with secret key agreement between X and Y. Based on this, we employ an easily-computed secret-key-agreement bound---intrinsic mutual information&mdashto quantify the three flow modalities in a variety of systems including asymmetric flows and financial markets.Comment: 11 pages; 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/ite.ht