Distributed Stochastic Subgradient Optimization Algorithms Over Random and Noisy Networks

We study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a communication link. We consider the distributed subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes. By stochastic Lyapunov method, convex analysis, algebraic graph theory and martingale convergence theory, it is proved that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely

State Estimation for Distributed and Hybrid Systems

This thesis deals with two aspects of recursive state estimation: distributed estimation and estimation for hybrid systems. In the first part, an approximate distributed Kalman filter is developed. Nodes update their state estimates by linearly combining local measurements and estimates from their neighbors. This scheme allows nodes to save energy, thus prolonging their lifetime, compared to centralized information processing. The algorithm is evaluated experimentally as part of an ultrasound based positioning system. The first part also contains an example of a sensor-actuator network, where a mobile robot navigates using both local sensors and information from a sensor network. This system was implemented using a component-based framework. The second part develops, a recursive joint maximum a posteriori state estimation scheme for Markov jump linear systems. The estimation problem is reformulated as dynamic programming and then approximated using so called relaxed dynamic programming. This allows the otherwise exponential complexity to be kept at manageable levels. Approximate dynamic programming is also used to develop a sensor scheduling algorithm for linear systems. The algorithm produces an offline schedule that when used together with a Kalman filter minimizes the estimation error covariance

Financial Market Models for the Grid

The existing network of computing devices around the world created by the Internet gives the possibility of establishing a global market for computing power, where anybody connected to this network can acquire computing power or sell his own spare computing resources in exchange for real money. This potential global market for computing power, which does not exist yet, is what we study in this thesis. Specifically, we study the market with both analytic and simulated models. This thesis predicts how a future global market for Grid computing will behave. We give arguments that such a large market, together with its potential indefinite growth, would not be able to scale if it were organized with a central server, and therefore we study a peer-to-peer market model in our simulations. We create a high-level model with the most relevant characteristics of the market, where buyers and sellers trade a single commodity. In our simulations, the parameters of the volume of contracts, proportion of satisfied agents and number of messages in the network achieve stable values in the long run. We also derive analytically the conditions that make the price get stable over time; we then implement these conditions in the simulation as local mechanisms of the market participants, which make the whole system achieve a stable price evolution. We are also confident that, as soon as the Grid market emerges, a parallel market of derivatives will be created as well. This market of derivatives will be important due to the non-storability nature of computing power. We develop a futures market for computing power based on Markov chains, where we initially model the behaviour of each participant with a particular Markov chain, and then we derive a global transition probability matrix that models the market as a whole. Furthermore, we analyse the performance of a futures trader operating in such a market, and we obtain an optimal trading strategy with the use of Markov Decision Processes. We finally develop a stochastic differential equation model that captures the essence of the spot price evolution of computing power observed in our market simulations. This model is based on a previously one proposed for the electricity market, and consists of the use of a Markov regime-switching mechanism in order to model the existence of spikes in the spot price. We then estimate the parameters in the model with the output data of our simulation program; the estimation is carried out both by maximum likelihood and the generalised method of moments

Finite-Time Thermodynamics

The theory around the concept of finite time describes how processes of any nature can be optimized in situations when their rate is required to be non-negligible, i.e., they must come to completion in a finite time. What the theory makes explicit is “the cost of haste”. Intuitively, it is quite obvious that you drive your car differently if you want to reach your destination as quickly as possible as opposed to the case when you are running out of gas. Finite-time thermodynamics quantifies such opposing requirements and may provide the optimal control to achieve the best compromise. The theory was initially developed for heat engines (steam, Otto, Stirling, a.o.) and for refrigerators, but it has by now evolved into essentially all areas of dynamic systems from the most abstract ones to the most practical ones. The present collection shows some fascinating current examples

Discretisation of continuous-time stochastic optimal control problems with delay

In the present work, we study discretisation schemes for continuous-time stochastic optimal control problems with time delay. The dynamics of the control problems to be approximated are described by controlled stochastic delay (or functional) differential equations. The value functions associated with such control problems are defined on an infinite-dimensional function space. The discretisation schemes studied are obtained by replacing the original control problem by a sequence of approximating discrete-time Markovian control problems with finite or finite-dimensional state space. Such a scheme is convergent if the value functions associated with the approximating control problems converge to the value function of the original problem. Following a general method for the discretisation of continuous-time control problems, sufficient conditions for the convergence of discretisation schemes for a class of stochastic optimal control problems with delay are derived. The general method itself is cast in a formal framework. A semi-discretisation scheme for a second class of stochastic optimal control problems with delay is proposed. Under standard assumptions, convergence of the scheme as well as uniform upper bounds on the discretisation error are obtained. The question of how to numerically solve the resulting discrete-time finite-dimensional control problems is also addressed

Discrete Event Simulations

Considered by many authors as a technique for modelling stochastic, dynamic and discretely evolving systems, this technique has gained widespread acceptance among the practitioners who want to represent and improve complex systems. Since DES is a technique applied in incredibly different areas, this book reflects many different points of view about DES, thus, all authors describe how it is understood and applied within their context of work, providing an extensive understanding of what DES is. It can be said that the name of the book itself reflects the plurality that these points of view represent. The book embraces a number of topics covering theory, methods and applications to a wide range of sectors and problem areas that have been categorised into five groups. As well as the previously explained variety of points of view concerning DES, there is one additional thing to remark about this book: its richness when talking about actual data or actual data based analysis. When most academic areas are lacking application cases, roughly the half part of the chapters included in this book deal with actual problems or at least are based on actual data. Thus, the editor firmly believes that this book will be interesting for both beginners and practitioners in the area of DES

Four Essays in Economic Theory

This thesis comprises four essays that belong to different strands of the theoretical economic literature. Chapter 1 and Chapter 2 study two-sided one-to-one matching markets with quasi-linear utility and multi-dimensional heterogeneity. Chapter 1 investigates the efficiency properties of two-sided investments and in particular the sources and limitations of potential investment coordination failures in large two-sided economies with competitive post-investment market. Chapter 2 scrutinizes a novel two-sided matching model with a finite number of agents and two-sided private information about exogenously given attributes. Chapter 3 is a note on the optimal size of fixed-prize research tournaments that seeks to fill two important gaps in an influential paper by Fullerton and McAfee (1999), and Chapter 4 studies the impact of incomplete information on the problem of maximizing revenue in a dynamic version of the knapsack problem, which is a classical combinatorial resource allocation problem with numerous economic applications

Robust load frequency control of interconnected grids with electric vehicles

This thesis presents new load frequency controls of interconnected grids, using electric vehicles to assist power plants in providing stability, which fluctuates with load demands and renewable powers. New robust control schemes for comprehensive power systems with electric vehicles, diverse transmission links, network-induced time delays and uncertainties are investigated.<br /