On the Limited Communication Analysis and Design for Decentralized Estimation

This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation~schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.Comment: Updates on the paper in CDC 201

Tools for producing formal specifications : a view of current architectures and future directions

During the last decade, one important contribution towards requirements engineering has been the advent of formal specification languages. They offer a well-defined notation that can improve consistency and avoid ambiguity in specifications. However, the process of obtaining formal specifications that are consistent with the requirements is itself a difficult activity. Hence various researchers are developing systems that aid the transition from informal to formal specifications. The kind of problems tackled and the contributions made by these proposed systems are very diverse. This paper brings these studies together to provide a vision for future architectures that aim to aid the transition from informal to formal specifications. The new architecture, which is based on the strengths of existing studies, tackles a number of key issues in requirements engineering such as identifying ambiguities, incompleteness, and reusability. The paper concludes with a discussion of the research problems that need to be addressed in order to realise the proposed architecture

Grammar-based Representation and Identification of Dynamical Systems

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model structure and complexity selection. In order to solve the combined model structure and model parameter estimation problem, a new representation of dynamical systems is proposed. The proposed representation is based on Tree Adjoining Grammar, a formalism that was developed from linguistic considerations. Using the proposed representation, the identification problem can be interpreted as a multi-objective optimization problem and we propose a Evolutionary Algorithm-based approach to solve the problem. A benchmark example is used to demonstrate the proposed approach. The results were found to be comparable to that obtained by state-of-the-art non-linear system identification methods, without making use of knowledge of the system description.Comment: Submitted to European Control Conference (ECC) 201

Collective Coordinate Control of Density Distributions

Real collective density variables $C(\boldsymbol{k})$ [c.f. Eq.\ref{Equation3})] in many-particle systems arise from non-linear transformations of particle positions, and determine the structure factor $S(\boldsymbol{k})$, where $\bf k$ denotes the wave vector. Our objective is to prescribe $C({\boldsymbol k})$ and then to find many-particle configurations that correspond to such a target $C({\bf k})$ using a numerical optimization technique. Numerical results reported here extend earlier one- and two-dimensional studies to include three dimensions. In addition, they demonstrate the capacity to control $S(\boldsymbol{k})$ in the neighborhood of $|\boldsymbol{k}| =$ 0. The optimization method employed generates multi-particle configurations for which $S(\boldsymbol{k}) \propto |\boldsymbol{k}|^{\alpha}$, $|\boldsymbol{k}| \leq K$, and $\alpha =$ 1, 2, 4, 6, 8, and 10. The case $\alpha =$ 1 is relevant for the Harrison-Zeldovich model of the early universe, for superfluid $^{4}{He}$, and for jammed amorphous sphere packings. The analysis also provides specific examples of interaction potentials whose classical ground state are configurationally degenerate and disordered.Comment: 26 pages, 8 figure

Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo