Nation-Building Modeling and Resource Allocation Via Dynamic Programming

Dynamic programming is used in many military and industrial applications to solve sequential decision making problems. This research proposes the development of a model and approach to address the application of dynamic programming in nation-building modeling. Through the creation of component indices to capture the state of operational variables: Political, Military, Economic, Social, Infrastructure, and Information (PMESII), a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power: Diplomatic, Informational, Military, and Economic (DIME). Solving this problem with dynamic programming provides an improved sequence which describes the application of DIME in a manner that minimizes an objective (i.e. cost, time) and allows the model to account for external factors such as an insurgent reaction to US policy. An application of the model is derived for Iraq to demonstrate the utility of the model and explore various aspects of the solution space. This modeling approach offers a potential significant capability when analyzing and planning for nation-building operations

Lanchester-Type Models of Warfare, Volume I

The Twentieth Century has been characterized by innumerable attempts to use the Scientific Method as a basis for policy planning in national and international affairs. The emergence of the field of operations research (OR) out of attempts of scientists in the Western Democracies to apply the Scientific Method to military problems during World War II is well known. Since World War II there has been a dramatic growth in both the interest in and use of OR and systems-analysis techniques for such purposes within the U.S. defense establish- ment, especially since the beginning of the so-called McNamara Era of defense planning. A concomitant trend has been an equally dramatic increase in both the number and variety of mathematical models used to support these analytical activities

Understanding the Instruments of National Power through a System of Differential Equations in a Counterinsurgency

Models that account for the progression of nation-building and the impacts of the instruments of national power -- Diplomacy, Informational, Military, and Economic effects -- are rare. This research proposes the development of such a model. Through the derivation of state indices for the operational variables of Political, Military, Economic, Social, Infrastructure, and Information, a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power. This methodology is a mean-field inverse problem which solves for the coefficients of the differential equations in a data-driven manner. Publicly available data are used to develop the indices and describe the instruments of national power. Applying mean-field theory allows the differential equations to be solved through a nonlinear program that derives minimum error-producing coefficients. An application of the model is derived for Operation Iraqi Freedom to demonstrate the utility as well as the effects of various alternate strategies, using the dynamics captured in the model. This modeling approach offers a potentially significant capability for analyzing and planning future Stabilization, Security, Transition, and Reconstruction Operations (STTRO)

A Methodological Framework for Parametric Combat Analysis

This work presents a taxonomic structure for understanding the tension between certain factors of stability for game-theoretic outcomes such as Nash optimality, Pareto optimality, and balance optimality and then applies such game-theoretic concepts to the advancement of strategic thought on spacepower. This work successfully adapts and applies combat modeling theory to the evaluation of cislunar space conflict. This work provides evidence that the reliability characteristics of small spacecraft share similarities to the reliability characteristics of large spacecraft. Using these novel foundational concepts, this dissertation develops and presents a parametric methodological framework capable of analyzing the efficacy of heterogeneous force compositions in the context of space warfare. This framework is shown to be capable of predicting a stochastic distribution of numerical outcomes associated with various modes of conflict and parameter values. Furthermore, this work demonstrates a general alignment in results between the game-theoretic concepts of the framework and Media Interaction Warfare Theory in terms of evaluating force efficacy, providing strong evidence for the validity of the methodological framework presented in this dissertation

Command-and-control (C2) theory : a challenge to control science

by Michael Athans

Environmental valuation, ecosystem services and aquatic species

The thesis consists of an introduction and four articles that can be read independently of each other. The common topic is environmental valuation and cost-benefit analysis. The applications relates to the growing concern of invasive species, and to waterpower externalities. In broad terms, all of the articles relates to water management. Article 1: "A Cost-Benefit analysis of introducing a non-native species: the case of signal crayfish in Sweden", assesses the economic impact of introducing the signal crayfish into a Swedish lake. Two scenarios are set up and compared. The first one assumes that there is no introduction of signal crayfish, so that the noble crayfish is preserved. In the second scenario, the signal crayfish is introduced, which immediately wipes out the entire stock of noble crayfish. The values of noble- and signal crayfish populations are measured as present values of their net future revenues. The values are than compared and net benefit of an introduction is calculated. The result indicate that net benefit of an introduction is positive if the intrinsic growth rate or the carrying capacity of the noble crayfish is below 40 % that of the signal crayfish. Article 2: "Assessing management options for weed control with demanders and non-demanders in a choice experiment", estimates the benefits of having a weed management program for a lake in Sweden, and then compares them with corresponding costs. The policy recommendation from a simple cost-benefit rule is to control the weed at some specific sites of the lake. This paper also suggest how to distinguish those that have a positive WTP for at least one of the attributes (demanders) from those that have zero WTP for all attributes (non-demanders). The advantage of the suggested approach is that it facilitates to more clearly distinguish between conditional and unconditional willingness to pay. The suggested approach could also overcome some of the problems in the literature with negative welfare measures. Article 3: "Assessing transfer errors in the benefit transfer method: An application of invasive weed management using choice experiment", tests the accuracy of transferring benefits of a weed management program from one lake to another using choice experiment. The transfer errors are assessed and the convergent validity hypothesis is tested. Estimating the accuracy of benefit transfer for weed management is policy relevant as there are a number of lakes in Sweden infested with the water weed. The convergent validity was rejected for three out of five welfare estimates with a ten per cent significance level. Article 4: "Willingness to pay for environmental improvements in hydropower regulated rivers", assesses the benefits of environmental improvements along hydropower regulated rivers using choice experiments. Remedial measures that improve the conditions for fish, benthic invertebrates and river-margin vegetation were found to have a significant welfare increasing impact. The results can be of value for the implementation of the Water Framework Directives in Sweden, which aims to reform the use of all surface water and ground water in the member states

Modeling and Analysis of Resolve and Morale for the `Long War\u27

In The Art of War, Sun Tzu begins by stating: War is a matter of vital importance to the State; the province of life or death; the road to survival or ruin. It is mandatory that it be thoroughly studied. Sun Tzu follow\u27s this opening by stating five fundamental factors a commander must master to be successful in combat. The first of these factors is moral influence which Sun Tzu defines as that which causes the people to be in harmony with their leaders, so they will accompany them in life and death without fear of mortal peril. In the face of the instant communication provided by satellites, 24 hour news media coverage, and other technological advances, this factor is even more relevant today. This research provides an analytic framework, based on the principles of fourth generation operations, capturing the effects of will and resolve of the combatant and population. The strategic level model investigates the long term impacts of asymmetric conflict. These results are primarily measured in the socio-political arena rather than the military battlefield. The model developed in this dissertation remains a model of conflict and combat. However, some of the impacts from the political, economic, and informational instruments of power are represented in the model through the dynamic adaptation of public resolve and combat spirit. To paraphrase Sun Tzu, war is vitally important and must be studied. Therefore, this dissertation puts forth a means to model key aspects of conflict in the `long war\u27

Application of differential games to problems of military conflict: Tactical allocation problems, Part I

The mathematical theory of deterministic optimal control/differential games is applied to the study of some tactical allocation problems for combat described by Lanchester-type equations of warfare. A solution procedure is devised for terminal control attrition games. H. K. Weiss' supporting weapon system game is solved and several extensions considered. A sequence of one-sided dynamic allocation problems is considered to study the dependence of optimal allocation policies upon model form. The solution is developed for variable coefficient Lanchester-type equations when the ratio of attrition rates is constant. Several versions of Bellman's continuous stochastic gold-mining problem are solved by the Pontryagin maximum principle, and their relationship to the attrition problems is discussed. A new dynamic kill potential is developed. Several problems from continuous review deterministic inventory theory are solved by the maximum principle.The Office of Naval Researchhttp://archive.org/details/applicationofdif00taylN

Advanced control and optimisation of DC-DC converters with application to low carbon technologies

Prompted by a desire to minimise losses between power sources and loads, the aim of this Thesis is to develop novel maximum power point tracking (MPPT) algorithms to allow for efficient power conversion within low carbon technologies. Such technologies include: thermoelectric generators (TEG), photovoltaic (PV) systems, fuel cells (FC) systems, wind turbines etc. MPPT can be efficiently achieved using extremum seeking control (ESC) also known as perturbation based extremum seeking control. The basic idea of an ESC is to search for an extrema in a closed loop fashion requiring only a minimum of a priori knowledge of the plant or system or a cost function. In recognition of problems that accompany ESC, such as limit cycles, convergence speed, and inability to search for global maximum in the presence local maxima this Thesis proposes novel schemes based on extensions of ESC. The first proposed scheme is a variance based switching extremum seeking control (VBS-ESC), which reduces the amplitude of the limit cycle oscillations. The second scheme proposed is a state dependent parameter extremum seeking control (SDP-ESC), which allows the exponential decay of the perturbation signal. Both the VBS-ESC and the SDP-ESC are universal adaptive control schemes that can be applied in the aforementioned systems. Both are suitable for local maxima search. The global maximum search scheme proposed in this Thesis is based on extensions of the SDP-ESC. Convergence to the global maximum is achieved by the use of a searching window mechanism which is capable of scanning all available maxima within operating range. The ability of the proposed scheme to converge to the global maximum is demonstrated through various examples. Through both simulation and experimental studies the benefit of the SDP-ESC has been consistently demonstrated