<p>The purpose of the research presented in this thesis is to better understand and improve direct transcription methods for stiff and state constrained optimal control problems. When some implicit Runge-Kutta methods are implemented as approximations to the dynamics of an optimal control problem, a loss of accuracy occurs when the dynamics are stiff or constrained. A new grid refinement strategy which exploits the variation of accuracy is discussed. In addition, the use of a residual function in place of classical error estimation techniques is proven to work well for stiff systems. Computational experience reveals the improvement in efficiency and reliability when the new strategies are incorporated as part of a direct transcription algorithm. For index three differential-algebraic equations, the solutions of some implicit Runge-Kutta methods may not converge. However, computational experience reveals apparent convergence for the same methods used when index three state inequality constraints become active. It is shown that the solution chatters along the constraint boundary allowing for better approximations. Moreover, the consistency of the nonlinear programming problem formed by a direct transcription algorithm using an implicit Runge-Kutta approximation is proven for state constraints of arbitrary index.<P>

<p>Horton, Kirk Gerritt. Fault Detection and Model Identification in Linear Dynamical Systems. (Under the direction of Dr. Stephen La Vern Campbell.) Linear dynamical systems, Ex'+Fx=f(t), in which E is singular, are useful in a wide variety of applications. Because of this wide spread applicability, much research has been done recently to develop theory for the design of linear dynamical systems. A key aspect of system design is fault detection and isolation (FDI). One avenue of FDI is via the multi-model approach, in which the parameters of the nominal, unfailed model of the system are known, as well as the parameters of one or more fault models. The design goal is to obtain an indicator for when a fault has occurred, and, when more than one type is possible, which type of fault it is. A choice that must be made in the system design is how to model noise. One way is as a bounded energy signal. This approach places very few restrictions on the types of noisy systems which can be addressed, requiring no complex modeling requirement. This thesis applies the multi-model approach to FDI in linear dynamical systems, modeling noise as bounded energy signals. A complete algorithm is developed, requiring very little on-line computation, with which nearly perfect fault detection and isolation over a finite horizon is attained. The algorithm applies techniques to convert complex system relationships into necessary and sufficient conditions for the solutions to optimal control problems. The first such problem provides the fault indicator via the minimum energy detection signal, while the second problem provides for fault isolation via the separating hyperplane. The algorithm is implemented and tested on a suite of examples in commercial optimization software. The algorithm is shownto have promise in nonlinear problems, time varying problems, and certain types of linear problems for which existing theory is not suitable.<P>

<p>The problem of finding a feasible solution to a system of linear inequalities arises in numerous contexts. In this dissertation, we consider solving a system of linear inequalities in view of unconstrained convex programming problems. Solution methods for solving systems with either finitely or infinitely many linear inequalities are proposed. Convergence properties and implementation issues are discussed. Some computational results are also included. <P>

<p>The primary objectives of this research are formulation and evaluation ofa Bayesian approach for selecting input models in discrete-eventstochastic simulation. This approach takes into account the model,parameter, and stochastic uncertainties that are inherent in mostsimulation experiments in order to yield valid predictive inferences aboutthe output quantities of interest. We use prior information to specify theprior plausibility of each candidate input model that adequately fits thedata, and to construct prior distributions on the parameters of eachmodel. We combine prior information with the likelihood function of thedata to compute the posterior model probabilities and the posteriorparameter distributions using Bayes' rule. This leads to a BayesianSimulation Replication Algorithm in which: (a) we estimate the parameteruncertainty by sampling from the posterior distribution of each model'sparameters on selected simulation runs; (b) we estimate the stochasticuncertainty by multiple independent replications of those selected runs;and (c) we estimate model uncertainty by weighting the results of (a) and(b) using the corresponding posterior model probabilities. We alsoconstruct a confidence interval on the posterior mean response from theoutput of the algorithm, and we develop a replication allocation procedurethat optimally allocates simulation runs to input models so as to minimizethe variance of the mean estimator subject to a budget constraint oncomputer time. To assess the performance of the algorithm, we propose someevaluation criteria that are reasonable within both the Bayesian andfrequentist paradigms. An experimental performance evaluation demonstratesthe advantages of the Bayesian approach versus conventional frequentisttechniques.<P>

<p>Successful e-commerce presupposes techniques by which autonomous trading entities can interoperate. Although much progress has been made on data exchange and payment protocols, interoperation in the face of autonomy is still inadequately understood. Current techniques, designed for closed environments, support only the simplest interactions.This dissertation concentrates on two themes. First, we develop a generic agent interaction model that supports agent coordination. We propose metacommitment patterns, which accommodate revisions and exceptions, to model agent interaction. We formalize metacommitment patterns declaratively in temporal logic. We apply statecharts to specify behavior models of agents who follow our commitment patterns. The statecharts provide an operational semantics, which can be used as a rigorous basis for agent coordination. We propose agent behavior models and prove that it operationally supports our temporal logic semantics. In this manner, we provide the basis for formally designing coordinated multiagent systems. Second, we apply agent behavior models for interoperation in e-commerce. This approach consists of (1) behavioral models to specify autonomous, heterogeneous agents representing different trading entities (businesses, consumers, brokers), (2) a metamodel that provides a language (based on XML) for specifying a variety of service agreements and accommodating exceptions and revisions, and (3) an execution architecture that supports persistent and dynamic (re)execution. Our implementation uses existing Java tool kits for parsing XML and building communicating agents. The main contributions of this dissertation are in developing some theoretical aspects of agent interaction with an emphasis on e-commerce.In addition, the proposed approach can also provide a rigorous basis for future standards for interoperation in e-commerce.<P>

<p> KARNOUB, RAZEK E. An Exact Bidirectional Approach to the Resource Constrained Project Scheduling Problem. (Under the direction of Salah E. Elmaghraby) The aim of this research is to develop a new approach to the Resource Constrained Project Scheduling Problem. Traditionally, most exact approaches to solve the problem have been either Integer Programming approaches or Branch and Bound (BaB) ones. Of the two, BaB procedures have proven to be the more successful computationally. But, while it is quite intuitive to conceive that the root node of a BaB search tree should be the start activity, it is no less conceivable that it be the terminal activity. Indeed, it is conceivable that the search starts from both ends and concludes somewhere in the middle of the ensuing trees. Unfortunately, BaB as a methodology is not amenable to deriving a termination criterion for such a procedure which guarantees optimality. To a large extent, this research can be seen as an attempt at accomplishing just that. We start with a comprehensive review of the literature related to the problem. We present a new Integer Programming model to describe it together with a `look-ahead' heuristic procedure which may be used along with it. The main advantage of this procedure is its ability to reflect planning over the short horizon in anticipation of changes to the project in the more future. Our chief contribution is in the third part of this study which sets up the problem as a Shortest Path Problem in two `state networks', forward and reverse, where the nodes reflect the precedence feasibility or partial completion of the activities of the project. We develop the conceptual tools to construct the networks and to properly detect a `path' between their sources from which a makespan optimal schedule could be derived. The theoretical constructs ultimately result in algorithms that solve the problem proceeding forward, in reverse, or bidirectionally. These algorithms have been tested on the J30 benchmark data set of Kolisch, Sprecher and Drexl (1995). Computational results show important advantages of the bidirectional approach but also point out significant avenues for improvement.<P>

<p>Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN iscomposed of individual automata that, for the most part, act independently, requiring only infrequentinteraction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum ofKronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN's compactrepresentation, known as the descriptor, is often outweighed by its tendency to make analysis of theunderlying Markov chain tough. Although iterative or projection methods have been used to solve the system P Q=0, the convergence to the stationary solution P is still unsatisfactory. SAN's compact representation hasmade the next logical research step of preconditioning thorny. Several preconditioners for SANs have beenproposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success ofapproximate inverses as preconditioners, we have explored their potential as SAN preconditioners. Onepromising finding on approximate inverse preconditioner is the nearest Kronecker product (NKP) approximationintroduced by Pitsianis and Van Loan. In this dissertation, we approximate Q by the nearest Kronecker productfor a SAN with a Kronecker product, A1 D A2 D . . . D AN. Then, we take M= A1-1 A2-1 D . . . D AN-1 as ourSAN NKP preconditioner. We show how successful this NKP preconditioner is for SANs by testing it on severalexamples. We also introduce and catalogue some new results about the Kronecker product, an operation which isfundamental to this SAN research.<P>

Thesis (Ph. D.)--Illinois State University, 2005. / Title from title page screen, viewed April 12, 2007. Dissertation Committee: Patricia H. Klass (chair), James C. Palmer, Stephen M. Bragg, Zeng Lin. Includes bibliographical references (leaves 168-179) and abstract. Also available in print.

This work addresses the problem of how an R&D section should decide on a strategy to guide its work when there is no strategic direction supplied from above by the company. The work includes a participant observer case study carried out over five years in a single R&D section, an analysis of research papers on the subject of management of section level R&D, and a review of textbooks on strategy, management and organisational behaviour. From the case study it was concluded that the company itself formed the strategic environment which the strategy of the R&D section had to address, and that the section’s strategic environment was chaotic in the mathematical sense. From the review of management textbooks it was concluded that standard theories do not give usable guidelines for the manager in this situation. A theory was developed that R&D strategy can be thought about in four distinctly different ways. Publications concentrate on two of these, while the case study and surveys of practising managers revealed that the other two were more pertinent in practice. The analysis of research papers was carried out using a newly developed technique, which showed that this body of literature is in a pre-paradigm state. The new technique was also used to show that the four different ways of thinking about R&D are present in the papers. The new literature analysis technique and the theory that R&D strategy can be thought about in four different way were tested by means of questionnaires filled in by authors of papers and by groups of R&D practitioners.

Although attention has been given to parental attitudes regarding enrollment of their high-risk infants in research, there is a paucity of knowledge in the literature, which investigates nurses’ experiences of caring for high-risk infants involved in research. Consequently, there is little understanding of how caring for these infants impacts nursing care. The purpose of this research was to arrive at an increased understanding of neonatal nurses' experiences in caring for high-risk infants involved in research. Attention was given to exploring neonatal intensive care unit (NICU) nurses’ perspectives towards neonatal research and the notion of risk to involving high-risk infants in research, their perceived roles and responsibilities with regards to high-risk infants in research, and the impact of research on caring for high-risk infants. This study was built on the research program of the student’s supervisor that seeks to increase the knowledge base of the nature of risk in child health research. An exploratory descriptive study within the qualitative paradigm was used. Seven semi-structured interviews, one focus group interview, and field notes were used to obtain information from seven NICU nurses. All of the qualitative data that emerged was analyzed using the constant comparative data analysis technique. Data analysis revealed that safeguarding their patients, or being a “safety net”, was the essence of nurses’ experiences of caring for high-risk infants involved in research. The nurses described their main role was the provision of a safe environment, regardless of the infants’ involvement in research. Acting as a “safety net” involved the nurses always being on guard and knowledgeable about their patients’ care. The following three themes further depicting the safeguarding experience emerged: feelings within, keeping it near and dear, and making it safer. The first theme, feelings within, uncovered nurses’ mixed emotions when caring for infants involved in research, which ranged from positive feelings to feelings of moral distress. The second theme, keeping it near and dear, referred to the uncomfortable feelings and memories that nurses held about situations in which they felt infants enrolled in research had suffered because of their inability of not being able to fully safeguard them. Some of the nurses expressed regretting their choices, such as not speaking up on a patient’s behalf, while others described it as a learning process, which eventually contributed to their abilities to safeguard infants. The third theme, making it safer, was based on the nurses’ enthusiasm about the future of neonatal research. The nurses identified many ways in which child health researchers, bedside nurses, REB members, and parents could minimize the risks of involving high-risk infants in research. This study yielded new insights about how NICU nurses care for high-risk infants involved in research that may be used to improve the protection of high-risk infants in research and ultimately contribute to the quality of care for these infants. Recommendations for nursing practice, education, and research are suggested. / October 2008