Robert Murphey

Frequency Assignment Problems

The term frequency assignment has been used to describe many types of problems which, quite often, have different modeling needs and objectives. These problems include: 1. Planning models for permanent spectrum allocation, licensing, and regulation which maximize utilization of all radio spectra [94]. 2. Planning models for network design within a given allocation to include; aeronautical mobile, land mobile, maritime mobile, broadcast, land fixed (point-to-point) and satellite. 3. On-line algorithms for dynamically assigning frequencies to users within an established network. Of special interest here are land cellular mobile systems, where an enormous amount of research has been done. A paper by Katzela and Naghshineh [55] contains nearly 100 references to works just in cellular dynamic channel assignment.

Theory and algorithms for cooperative systems

Over the past several years, cooperative control and optimization have increasingly played a larger and more important role in many aspects of military sciences, biology, communications, robotics, and decision making. At the same time, cooperative systems are notoriously difficult to model, analyze, and solve - while intuitively understood, they are not axiomatically defined in any commonly accepted manner. The works in this volume provide outstanding insights into this very complex area of research. They are the result of invited papers and selected presentations at the Fourth Annual Conference on Cooperative Control and Optimization held in Destin, Florida, November 2003.

A Parallel Grasp for the Data Association Multidimensional Assignment Problem

Data association multidimensional assignment problems appear in many applications such as MultiTarget MultiSensor Tracking, and particle tracking. The problem is characterized by the large input data and is very difficult to solve exactly. A Greedy Randomized Adaptive Search Procedure (GRASP) has been developed and computational results show good quality solutions can be obtained. Furthermore, the efficiency of the GRASP can be easily improved by parallelization of the code in the MPI environment.

Robust Decision Making: Addressing Uncertainties in Distributions

This paper develops a general approach to risk management in military applications involving uncertainties in information and distributions. The risk of loss, damage, or failure is measured by the Conditional Value-at-Risk (CVaR) measure. Loosely speaking, CVaR with the confidence level α estimates the risk of loss by averaging the possible losses over the (1 - α) · 100% worst cases (e.g., 10%). As a function of decision variables, CVaR is convex and therefore can be efficiently controlled/optimized using convex or (under quite general assumptions) linear programming. The general methodology was tested on two Weapon-Target Assignment (WTA) problems. It is assumed that the distributions of random variables in the WTA formulations are not known with certainty. The total cost of a mission (including weapon attrition) was minimized, while satisfying operational constraints and ensuring destruction of all targets with high probabilities. The risk of failure of the mission (e.g., targets are not destroyed) is controlled by CVaR constraints. The case studies conducted show that there are significant qualitative and quantitative differences in solutions of deterministic WTA and stochastic WTA problems.

Detection of temporal changes in psychophysiological data using statistical process control methods

We consider the problem of detecting temporal changes in the functional state of human subjects due to varying levels of cognitive load using real-time psychophysiological data. The proposed approach relies on monitoring several channels of electroencephalogram (EEG) and electrooculogram (EOG) signals using the methods of statistical process control. It is demonstrated that control charting methods are capable of detecting changes in psychophysiological signals that are induced by varying cognitive load with high accuracy and low false alarm rates, and are capable of accommodating subject-specific differences while being robust with respect to differences between different trials performed by the same subject.

An algorithm for online detection of temporal changes in operator cognitive state using real-time psychophysiological data

Abstract We consider the problem of on-the-fly detection of temporal changes in the cognitive state of human subjects due to varying levels of difficulty of performed tasks using real-time EEG and EOG data. We construct the Cognitive State Indicator (CSI) as a function that projects the multidimensional EEG/EOG signals onto the interval [0,1] by maximizing the Kullback–Leibler distance between distributions of the signals, and whose values change continuously with variations in cognitive load. During offline testing (i.e., when evolution in time is disregarded) it was demonstrated that the CSI can serve as a statistically significant discriminator between states of different cognitive loads. In the online setting, a trend detection heuristic (TDH) has been proposed to detect real-time changes in the cognitive state by monitoring trends in the CSI. Our results support the application of the CSI and the TDH in future closed-loop control systems with human supervision.

Use of Conditional Value-at-Risk in Stochastic Programs with Poorly Defined Distributions

On the example of the Weapon-Target Assignment (WTA) problem, we present risk management procedures for military applications that address uncertainties in distributions. In the considered formulation, the cumulative damage to the targets is maximized, which leads to Mixed-Integer Programming problems with non-linear objectives. Ву using a relaxation technique that preserves integrality of the optimal solutions, we developed LP formulations for the deterministic and two-stage stochastic WTA problems. The risk of incorrect second-stage decisions due to errors in specified distributions of the second-stage targets is controlled using the Conditional Value-at-Risk risk measure. An LP formulation for the two-stage SWTA problem with uncertainties in distributions has been developed, which produces integer optimal solutions for the first-stage decision variables, and also yields a tight lower bound for the corresponding MIP problem.

Dynamics of Information Systems: Mathematical Foundations

This book presents recent developments and results found by participants of the Third International Conference on the Dynamics of Information Systems, which took place at the University of Florida, Gainesville FL, USA on February 16-18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in a broad range of topics relevant to the theory and practice of the dynamics of information systems.Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic, and military systems must be better understood to achieve large advances in the capability and understanding of these systems. Applications are widespread and include: research in evolutionary theory, optimization of information workflow, military applications, climate networks, collision work, and much more.Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic, and military systems must be better understood to achieve large advances in the capability and understanding of these systems. Applications are widespread and include: research in evolutionary theory, optimization of information workflow, military applications, climate networks, collision work, and much more.

Modeling and Implementation of Risk-Averse Preferences in Stochastic Programs Using Risk Measures

We consider modeling and implementation of risk-averse preferences in stochastic programming problems using axiomatically defined risk measures. We derive representations for several classes of risk measures (e.g., coherent risk measures, deviation measures) via solutions of specially formulated stochastic programming problems that facilitate incorporation of risk measures in multistage stochastic programming problems. As an illustration of the general approach, we consider a two-stage stochastic weapon-target assignment problem, where a coherent risk measure is used to capture the risk of the second-stage (recourse) action.

Optimization of convergence rate and stability margin of information flow in cooperative systems

The interplay between the convergence rate and stability margin (e.g. ability to reject disturbances) for a discrete-time information flow filter in cooperative systems is analyzed. For a given communication graph, the convergence rate is defined as the absolute value of the largest nonunit characteristic root of a matrix associated with the filter. The maximal convergence rate, obtained by “tuning” the control gains, is highly correlated to the number of distinct eigenvalues of the graph Laplacian (it is 1 for the complete graph). A stability margin is introduced for multiple-input–multiple-output (MIMO) systems and is then maximized with respect to the control gains subject to a constraint on the convergence rate. The optimal stability margin as a function of the convergence rate is bounded above for any order of the filter, and the bound is attained for the complete graph. For the zero-order filter and all strongly connected communication graphs, the optimal stability margin is found analytically, whereas for the first-order filter and undirected communication graphs, it is evaluated numerically. The results demonstrate the ability to distinguish graph topologies that dominate others in their ability to reject disturbances and converge rapidly to a consensus.