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Dissertations / Theses on the topic 'Control theory and applications'

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Published: 10 December 2022
Last updated: 19 February 2023

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1

Al-Assaf, Y. "Self-tuning control : Theory and applications." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235033.

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2

Tonita, Robert Jon. "Applications of control theory to economics." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608803.

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3

May, B. Scott. "Probabilistic robust control : theory and applications." Diss., Pasadena, Calif. : California Institute of Technology, 1998. http://resolver.caltech.edu/caltechEERL:1997.EERL-97-08.

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4

Forrest, Stephen Wilson. "Self-tuning LQG control : theory and applications." Thesis, University of Strathclyde, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284279.

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5

Zenios, Stefanos A. (Stefanos Andrea). "Health care applications of optimal control theory." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/11042.

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6

Fukao, Takanori. "Studies on adaptive control theory and its applications." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/150622.

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7

Huzmezan, Mihai. "Theory and aerospace applications of constrained model based predictive control." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/272419.

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8

Gordon, Dinah Rose. "Applications of nonstandard analysis in differential game theory." Thesis, University of Hull, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318386.

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9

Mendel, Max B. "Development of Bayesian parametric theory with applications to control." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/14302.

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10

Heffernan, Donal A. "Embedded real-time networks for control applications." Thesis, University of Salford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272619.

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11

Mutib, Khalid N. "Real-time, construction and applications of a transputer embedded controler : with applications in pneumatic servo and mobile robot." Thesis, University of Reading, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.339490.

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12

Wu, Dong-Nan. "Active bounded-state vibration control for structural applications." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/12326.

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13

Härkegård, Ola. "Backstepping and control allocation with applications to flight control." Doctoral thesis, Linköpings universitet, Institutionen för systemteknik, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-23177.

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In this thesis we study a number of nonlinear control problems motivated by their appearance in flight control. The results are presented in a general framework and can also be applied to other areas. The two main topics are backstepping and control allocation. Backstepping is a nonlinear control design method that provides an alternative to feedback linearization. Here, backstepping is used to derive robust linear control laws for two nonlinear systems, related to angle of attack control and flight path angle control, respectively. The resulting control laws require less modeling information than corresponding designs based on feedback linearization, and achieve global stability in cases where feedback linearization can only be performed locally. Further, a method for backstepping control of a rigid body is developed, based on a vector description of the dynamics. We also discuss how to augment an existing nonlinear controller to suppress constant input disturbances. Two methods, based on adaptive backstepping and nonlinear observer design, are proposed. Control allocation deals with actuator utilization for overactuated systems. In this thesis we pose the control allocation problem as a constrained least squares problem to account for actuator position and rate constraints. Efficient solvers based on active set methods are developed with similar complexity to existing, approximate, pseudoinverse methods. A method for dynamic control allocation is also proposed which enables a frequency dependent control distribution among the actuators to be designed. Further, the relationship between control allocation and linear quadratic control is investigated. It is shown that under certain circumstances, the two techniques give the same freedom in distributing the control effort among the actuators. An advantage of control allocation, however, is that since the actuator constraints are considered, the control capabilities of the actuator suite can be fully exploited.
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14

Wang, Junmin, and 王軍民. "Riesz basis property of some infinite-dimensional control problems andits applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B3016350X.

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15

Kuypers, Karl-Heinz. "An investigation into series controller applications and control-algorithms." Thesis, Staffordshire University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300952.

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16

Grout, Ian Andrew. "The systematic design of ASICs for control system applications." Thesis, Lancaster University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239064.

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17

Axelsson, Henrik. "Optimal Control of Switched Autonomous Systems: Theory, Algorithms, and Robotic Applications." Diss., Available online, Georgia Institute of Technology, 2006, 2006. http://etd.gatech.edu/theses/available/etd-04052006-131248/.

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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006.
Ashraf Saad, Committee Member ; Spyros Reveliotis, Committee Member ; Anthony Yezzi, Committee Member ; Erik Verriest, Committee Member ; Yorai Wardi, Committee Co-Chair ; Magnus Egerstedt, Committee Chair.
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18

James, Courtney D. "The design of robust multi-rate repetitive learning controllers with applications to practical systems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/16104.

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19

Saddique, Syed Mohammad. "Fine-tuned QFT controller design and applications to robot manipulators." Thesis, University of Newcastle Upon Tyne, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.238867.

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20

Papageorgiou, George. "Robust control system design : H∞ loop sharing and aerospace applications." Thesis, University of Cambridge, 1998. https://www.repository.cam.ac.uk/handle/1810/272494.

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21

Zhang, Lei. "Stochastic optimal control and regime switching : applications in economics." Thesis, University of Warwick, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.387250.

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22

Rogers, Walter L. "Applications of modern control theory synthesis to a super-augmented aircraft." Thesis, Monterey, California. Naval Postgraduate School, 1989. http://hdl.handle.net/10945/26890.

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23

Fize, Florian. "From Theory to Implementation of Embedded Control Applications : A Case Study." Thesis, Linköpings universitet, Institutionen för datavetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-131256.

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Control applications are used in almost all scientific domains and are subject to timing constraints. Moreover, different applications can run on the same platform which leads to even more complex timing behaviors. However, some of the timing issues are not always considered in the implementation of such applications, and this can make the system fail. In this thesis, the timing issues are considered, i.e., the problem of non-constant delay in the control of an inverted pendulum with a real-time kernel running on an ATmega328p micro-controller. The study shows that control performance is affected by this problem. In addition, the thesis, reports the adaptation of an existing real-time kernel based on an EDF (Earliest Deadline First) scheduling policy, to the architecture of the ATmega328p. Moreover, the new approach of a server-based kernel is implemented in this thesis, still on the same Atmel micro-controller.
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24

Scarciotti, Giordano. "Approximation, analysis and control of large-scale systems : theory and applications." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/30781.

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This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.
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25

Copsey, Darryl Richard. "Robust stabilisation of linear systems with applications to tokamak plasma control." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264936.

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26

Littleboy, Darren M. "Numerical techniques for eigenstructure assignment by output feedback in aircraft applications." Thesis, University of Reading, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259495.

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27

Juniper, James. "A Keynesian critique of recent finance and macroeconomic applications of risk-sensitive and robust control theory." Title page, contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phj953.pdf.

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Bibliography: leaves 479-544. The objective of this thesis is to assess the strengths and weaknesses of recent economic applications of robust and risk-sensitive control theory from a Keynesian perspective.
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28

Nomikos, Panagiotis. "Multivariable self-tuning controllers for industrial applications." Thesis, University of Sussex, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235577.

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29

Abdallah, C. T. (Chaouki T. ). "Robust control and game theory for nonlinear systems with applications to robotics." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/14885.

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30

Álvarez, Martín José Alberto. "Adaptive multivariable intermittent control : theory, development, and applications to real-time systems." Thesis, University of Glasgow, 2018. http://theses.gla.ac.uk/30633/.

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Intermittent Control, as a control scheme that switches between open and closed-loop configurations, has been suggested as an alternative model to describe human control and to explain the intermittency observed during sustained control tasks. Additionally, IC might be beneficial in the following scenarios: 1 - in the field of robotics, where open-loop evolution could be used for computationally intensive tasks such as constrained optimisation routines, 2 - in an adaptation context, helping to detect system and environmental variations. Based on these ideas, this thesis explored the application of real-time multivariable intermittent controllers in humanoid robotics as well as adaptive versions of IC implemented on inverted pendulum structures.
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31

Iamratanakul, Dhanakorn. "Pre-actuation and post-actuation in control applications /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/9968.

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32

Hunt, K. J. "Stochastic optimal control theory with application in self-tuning control." Thesis, University of Strathclyde, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382399.

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33

Ni, Lingfei. "Classic optimal control in continuous time with applications in economics." Kansas State University, 2014. http://hdl.handle.net/2097/18391.

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Master of Arts
Department of Economics
Steven P. Cassou
This report shows the mathematics behind the solution to continuous time optimization problems. It shows how to specify the Hamiltonian function, how to use the Hamiltonian to obtain the optimal conditions for a typical economic optimal control problem and applies these techniques to several optimal control problems commonly encountered in macroeconomics. An appendix shows how to set up the optimal conditions for the case in which the state and co-state variables are both vectors. A second appendix shows how to approach the control situation for a system of optimal control problems where the co-state variable for the first sub-optimal control problem is the state variable for the second sub-optimal control problem.
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34

Schön, Thomas B. "Estimation of Nonlinear Dynamic Systems : Theory and Applications." Doctoral thesis, Linköpings universitet, Reglerteknik, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7124.

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This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied. The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing. The nonlinear state estimation problem is addressed using sequential Monte Carlo methods, commonly referred to as particle methods. When there is a linear sub-structure inherent in the underlying model, this can be exploited by the powerful combination of the particle filter and the Kalman filter, presented by the marginalized particle filter. This algorithm is also known as the Rao-Blackwellized particle filter and it is thoroughly derived and explained in conjunction with a rather general class of mixed linear/nonlinear state-space models. Models of this type are often used in studying positioning and target tracking applications. This is illustrated using several examples from the automotive and the aircraft industry. Furthermore, the computational complexity of the marginalized particle filter is analyzed. The parameter estimation problem is addressed for a relatively general class of mixed linear/nonlinear state-space models. The expectation maximization algorithm is used to calculate parameter estimates from batch data. In devising this algorithm, the need to solve a nonlinear smoothing problem arises, which is handled using a particle smoother. The use of the marginalized particle filter for recursive parameterestimation is also investigated. The applications considered are the camera positioning problem arising from augmented reality and sensor fusion problems originating from automotive active safety systems. The use of vision measurements in the estimation problem is central to both applications. In augmented reality, the estimates of the camera’s position and orientation are imperative in the process of overlaying computer generated objects onto the live video stream. The objective in the sensor fusion problems arising in automotive safety systems is to provide information about the host vehicle and its surroundings, such as the position of other vehicles and the road geometry. Information of this kind is crucial for many systems, such as adaptive cruise control, collision avoidance and lane guidance.
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35

Wu, Min. "Multimedia data transmission for mobile wireless applications." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4132.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 14, 2006) Vita. Includes bibliographical references.
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36

Park, Baeil P. "Canonical forms for time-varying multivariable linear systems and periodic filtering and control applications." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/16734.

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37

Banisch, Ralf [Verfasser]. "Markov Processes Beyond Equilibrium and Optimal Control : Theory, Applications, and Examples / Ralf Banisch." Berlin : Freie Universität Berlin, 2015. http://d-nb.info/1078261687/34.

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38

Weston, Stephen Peter. "Applications of robust optimal control to decision making in the presence of uncertainty." Thesis, City University London, 2005. http://openaccess.city.ac.uk/8465/.

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This thesis is concerned with robustness of decision making in financial economics. Feedback control models developed in engineering are applied to three separate though linked problems in order to examine the role and impact of robustness in the creation and application of decision rules. Three problems are examined using robust optimal control techniques to evaluate the impact of robustness and stability in financial economic models. The first problem examines the use of linear models of robust optimal control in the pricing of castastrophe based derivatives and finds its relative performance to be superior to the popular jump diffusion and stochastic volatility models in the pricing of these emerging instruments. The novelty of the approach arises from the examination of the impact of robustness and stability of the pricing solution. The second problem involves robustness and stability of hedging. An alternative method of creating hedging rules is developed. The method is based on robust control Lyapunov functions that are simple, robust and stable in operation, yet in practice are not so conservative that they eliminate all trading gains. The third problem involves the development of robust control policies for managing risk, using non-linear robust optimal control techniques to provide clear evidence of superior performance of robust models when compared with existing VAR and EVT approaches to risk management. The novelty in the approach arises from the development of a simple and powerful risk management metric.
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39

Zhao, Xiaodong. "Orthonormal rational functions via the jury table and their applications /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?ELEC%202004%20ZHAO.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004.
Includes bibliographical references (leaves 124-130). Also available in electronic version. Access restricted to campus users.
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40

Maharaj, Davendra Yukteshwar. "The application of nonlinear control theory to robust helicopter flight control." Thesis, Imperial College London, 1994. http://hdl.handle.net/10044/1/7420.

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41

Simon, Daniel. "Fighter Aircraft Maneuver Limiting Using MPC : Theory and Application." Doctoral thesis, Linköpings universitet, Reglerteknik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-139945.

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Flight control design for modern fighter aircraft is a challenging task. Aircraft are dynamical systems, which naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems is becoming increasingly important as the performance and complexity of the aircraft is constantly increasing. The aeronautical industry has traditionally applied feedforward, anti-windup or similar techniques and different ad hoc engineering solutions to handle constraints on the aircraft. However these approaches often rely on engineering experience and insight rather than a theoretical foundation, and can often require a tremendous amount of time to tune. In this thesis we investigate model predictive control as an alternative design tool to handle the constraints that arises in the flight control design. We derive a simple reference tracking MPC algorithm for linear systems that build on the dual mode formulation with guaranteed stability and low complexity suitable for implementation in real time safety critical systems. To reduce the computational burden of nonlinear model predictive control we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefit of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence. An alternative to deriving MPC algorithms with guaranteed stability properties is to analyze the closed loop stability, post design. Here we focus on deriving a tool based on Mixed Integer Linear Programming for analysis of the closed loop stability and robust stability of linear systems controlled with MPC controllers. To test the performance of model predictive control for a real world example we design and implement a standard MPC controller in the development simulator for the JAS 39 Gripen aircraft at Saab Aeronautics. This part of the thesis focuses on practical and tuning aspects of designing MPC controllers for fighter aircraft. Finally we have compared the MPC design with an alternative approach to maneuver limiting using a command governor.
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42

Ghorbani, a. "Cross polar cancellation in satellite microwave systems : New practical designs and applications of propagation theory." Thesis, University of Bradford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376711.

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43

Noronha, Moreira Antunes Gomes Susana. "Control theory for infinite dimensional dynamical systems and applications to falling liquid film flows." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/39041.

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In this thesis, we study the problem of controlling the solutions of various nonlinear PDE models that describe the evolution of the free interface in thin liquid films flowing down inclined planes. We propose a control methodology based on linear feedback controls, which are proportional to the deviation between the current state of the system and a prescribed desired state. We first derive the controls for weakly nonlinear models such as the Kuramoto-Sivashinsky equation and some of its generalisations, and then use the insight that the analytical results obtained there provide us to derive suitable generalisations of the controls for reduced-order long-wave models. We use two long-wave models to test our controls: the first order Benney equation and the first order weighted-residual model, and compare some linear stability results with the full 2-D Navier-Stokes equations. We find that using point actuated controls it is possible to stabilise the full range of solutions to the generalised Kuramoto-Sivashinsky equation, and that distributed controls have a similar effect on both long-wave models. Furthermore, point-actuated controls are efficient when stabilising the flat solution of both long-wave models. We extend our results to systems of coupled Kuramoto-Sivashinsky equations and to stochastic partial differential equations that arise by adding noise to the weakly nonlinear models.
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44

Kang, Yong-Ho. "Adaptive control via genetic algorithms : theory and application." Thesis, University of Reading, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308023.

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45

Potocki, Jon Kyle. "Application of control theory to the hyperthermia problem." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185999.

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The objective of a hyperthermia cancer treatment is to heat the tumor tissue to a therapeutic level while limiting the detrimental effects experienced by the surrounding normal tissue. To achieve an optimal treatment requires knowledge of the resulting temperature response and an understanding of the complex interaction between the thermal response, the applied power, and the blood flow in the target tissue region. This dissertation considers model reduction to overcome the large dimensions associated with thermal modelling, extended Kalman filtering to estimate both the unmeasured temperature states and the unknown blood perfusion magnitudes, optimization of the applied power to achieve the best thermal response, and optimal servomechanism control to attain the desired regulated output tracking. A controller methodology that combines thermal estimation, applied power optimization, and optimal servomechanism control with a simple expert system shell is examined. This controller methodology is analyzed for a simulated scanned focussed ultrasound system (SFUS) based upon the bioheat transfer equation (BHTE) model of the thermal response in the target region. The results of the presented studies illustrate the following important points. First, open-loop reduced-order models based on the balanced transformation provide drastic model reduction for controller design purposes. Second, the success of thermal estimation depends on the number and the location of the thermal sensors, and the accuracy of the modelled blood perfusion profile. Third, multiple modelling in estimation provides an alternate technique for overcoming model mismatch associated with the modelling of the blood perfusion pattern. Fourth, the choice of the set points for the optimal servomechanism controller play a crucial role in the resulting tissue temperatures. Fifth, the scan parameter sets that result in optimal SFUS power profiles need to be changed on-line during a treatment as the blood perfusion magnitude and pattern are estimated. Finally, to fully automate a hyperthermia treatment requires that the expertise of the clinician be incorporated into the controller design. Hierarchical control provides a means of incorporating the expert system shell at the higher levels of the controller, while maintaining optimal servomechanism control at the lower levels.
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46

Galbraith, Grant N. "Applications of variational analysis to optimal trajectories and nonsmooth Hamilton-Jacobi theory /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5766.

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47

Sartipi, Mina. "Modern Error Control Codes and Applications to Distributed Source Coding." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/19795.

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This dissertation first studies two-dimensional wavelet codes (TDWCs). TDWCs are introduced as a solution to the problem of designing a 2-D code that has low decoding- complexity and has the maximum erasure-correcting property for rectangular burst erasures. The half-rate TDWCs of dimensions N1 X N2 satisfy the Reiger bound with equality for burst erasures of dimensions N1 X N2/2 and N1/2 X N2, where GCD(N1,N2) = 2. Examples of TDWC are provided that recover any rectangular burst erasure of area N1N2/2. These lattice-cyclic codes can recover burst erasures with a simple and efficient ML decoding. This work then studies the problem of distributed source coding for two and three correlated signals using channel codes. We propose to model the distributed source coding problem with a set of parallel channel that simplifies the distributed source coding to de- signing non-uniform channel codes. This design criterion improves the performance of the source coding considerably. LDPC codes are used for lossless and lossy distributed source coding, when the correlation parameter is known or unknown at the time of code design. We show that distributed source coding at the corner point using LDPC codes is simplified to non-uniform LDPC code and semi-random punctured LDPC codes for a system of two and three correlated sources, respectively. We also investigate distributed source coding at any arbitrary rate on the Slepian-Wolf rate region. This problem is simplified to designing a rate-compatible LDPC code that has unequal error protection property. This dissertation finally studies the distributed source coding problem for applications whose wireless channel is an erasure channel with unknown erasure probability. For these application, rateless codes are better candidates than LDPC codes. Non-uniform rateless codes and improved decoding algorithm are proposed for this purpose. We introduce a reliable, rate-optimal, and energy-efficient multicast algorithm that uses distributed source coding and rateless coding. The proposed multicast algorithm performs very close to network coding, while it has lower complexity and higher adaptability.
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48

Gaunard, Frédéric. "Problèmes d’interpolation dans les espaces de Paley-Wiener et applications en théorie du contrôle." Thesis, Bordeaux 1, 2011. http://www.theses.fr/2011BOR14371/document.

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Nous étudions des problèmes d'interpolation dans des espaces de fonctions analytiques et notamment les espaces de Paley-Wiener.Nous démontrons que l'opérateur de restriction associé à une suite de nombres complexes supposée a priori N-Carleson dans tout demi-plan, définit un isomorphisme entre l'espace de Paley-Wiener et un certain espace de suites (construit à l'aide de différences divisées) si et seulement si la suite en question vérifie certaines conditions, notamment la condition de Muckenhoupt. Ce résultat généralise un résultat de Lyubarskii et Seip de 1997.Nous montrons également que toute suite minimale dans l'espace de Paley-Wiener et telle que l'intersection avec tout demi-plan vérifie la condition de Carleson, est une suite d'interpolation dans tout espace de Paley-Wiener "plus grand", au sens du type exponentiel. Ce dernier résultat s'étend à l'interpolation pondérée et s'applique à la Théorie du contrôle
We study interpolation problems in spaces of analytic functions and in particular in Paley-Wiener spaces.We show that the restriction operator associated to some N-Carleson sequence is an isomorphism between the Paley-Wiener space and a certain space of sequences (contructed with the help of divided differences) if and only if the sequence satisfies some conditions, in particular the Muckenhoupt condition. This result is a generalization of a theorem of Lyubarskii and Seip obtained in 1997.We also show that every minimal sequence in PW such that the intersection with every half-plane satisfies the Carleson condition is actually an interpolating sequence in every “bigger” space in the sense of the exponential type. This result can be extended to weighted interpolation and has an application in Control Theory
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49

Graham, Marien Alet. "Contributions to the theory and applications of univariate distribution-free Shewhart, CUSUM and EWMA control charts." Thesis, University of Pretoria, 2013. http://hdl.handle.net/2263/32971.

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Abstract:
Distribution-free (nonparametric) control charts can be useful to the quality practitioner when the underlying distribution is not known. The term nonparametric is not intended to imply that there are no parameters involved, in fact, quite the contrary. While the term distribution-free seems to be a better description of what we expect from these charts, that is, they remain valid for a large class of distributions, nonparametric is perhaps the term more often used. In the statistics literature there is now a rather vast collection of nonparametric tests and confidence intervals and these methods have been shown to perform well compared to their normal theory counterparts. Remarkably, even when the underlying distribution is normal, the efficiency of some nonparametric tests relative to the corresponding (optimal) normal theory methods can be as high as 0.955 (see e.g. Gibbons and Chakraborti (2010) page 218). For some other heavy-tailed and skewed distributions, the efficiency can be 1.0 or even higher. It may be argued that nonparametric methods will be ‘less efficient’ than their parametric counterparts when one has a complete knowledge of the process distribution for which that parametric method was specifically designed. However, the reality is that such information is seldom, if ever, available in practice. Thus it seems natural to develop and use nonparametric methods in statistical process control (SPC) and the quality practitioners will be well advised to have these techniques in their toolkits. In this thesis we only propose univariate nonparametric control charts designed to track the location of a continuous process since very few charts are available for monitoring the scale and simultaneously monitoring the location and scale of a process. Chapter 1 gives a brief introduction to SPC and provides background information regarding the research conducted in this thesis. This will aid in familiarizing the reader with concepts and terminology that are helpful to the following chapters. Details are given regarding the three main classes of control charts, namely the Shewhart chart, the cumulative sum (CUSUM) chart and the exponentially weighted moving average (EWMA) chart. We begin Chapter 2 with a literature overview of Shewhart-type Phase I control charts followed by the design and implementation of these charts. A nonparametric Shewhart-type Phase I control chart for monitoring the location of a continuous variable is proposed. The chart is based on the pooled median of the available Phase I samples and the charting statistics are the counts (number of observations) in each sample that are less than the pooled median. The derivations recognize that in Phase I the signalling events are dependent and that more than one comparison is © University of Pretoria v made against the same estimated limits simultaneously; this leads to working with the joint distribution of a set of dependant random variables. An exact expression for the false alarm probability is given in terms of the multivariate hypergeometric distribution and this is used to provide tables for the control limits. Some approximations are discussed in terms of the univariate hypergeometric and the normal distributions. In Chapter 3 Phase II control charts are introduced and considered for the case when the underlying parameters of the process distribution are known or specified. This is referred to as the ‘standard(s) known’ case and is denoted Case K. Two nonparametric Phase II control charts are considered in this chapter, with the first one being a nonparametric exponentially weighted moving average (NPEWMA)-type control chart based on the sign (SN) statistic. A Markov chain approach (see e.g. Fu and Lou (2003)) is used to determine the run-length distribution of the chart and some associated performance characteristics (such as the average, standard deviation, median and other percentiles). In order to aid practical implementation, tables are provided for the chart’s design parameters. An extensive simulation study shows that on the basis of minimal required assumptions, robustness of the in-control run-length distribution and out-of-control performance, the proposed NPEWMA-SN chart can be a strong contender in many applications where traditional parametric charts are currently used. Secondly, we consider the NPEWMA chart that was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see e.g. Gibbons and Chakraborti (2010) page 195). This is called the nonparametric exponentially weighted moving average signed-rank (NPEWMA-SR) chart. In their article important questions remained unanswered regarding the practical implementation as well as the performance of this chart. In this thesis we address these issues with a more in-depth study of the NPEWMA-SR chart. A Markov chain approach is used to compute the run-length distribution and the associated performance characteristics. Detailed guidelines and recommendations for selecting the chart’s design parameters for practical implementation are provided along with illustrative examples. An extensive simulation study is done on the performance of the chart including a detailed comparison with a number of existing control charts. Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors. In Chapter 4 Phase II control charts are introduced and considered for the case when the underlying parameters of the process distribution are unknown and need to be estimated. This is referred to as the ‘standard(s) unknown’ case and is denoted Case U. Two nonparametric Phase II control charts are proposed in this chapter. They are a Phase II NPEWMA-type control chart and a nonparametric cumulative sum (NPCUSUM)-type control chart, based on the exceedance statistics, © University of Pretoria vi respectively, for detecting a shift in the location parameter of a continuous distribution. The exceedance statistics can be more efficient than rank-based methods when the underlying distribution is heavy-tailed and / or right-skewed, which may be the case in some applications, particularly with certain lifetime data. Moreover, exceedance statistics can save testing time and resources as they can be applied as soon as a certain order statistic of the reference sample is available. We also investigate the choice of the order statistics (percentile), from the reference (Phase I) sample that defines the exceedance statistic. It is observed that other choices, such as the third quartile, can play an important role in improving the performance of these exceedance charts. It is seen that these exceedance charts perform as well as and, in many cases, better than its competitors and thus can be a useful alternative chart in practice. Chapter 5 wraps up this thesis with a summary of the research carried out and offers concluding remarks concerning unanswered questions and / or future research opportunities. © University
Thesis (PhD)--University of Pretoria, 2013.
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Statistics
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50

Atkinson, D. J. "The application of estimation theory to induction motor control." Thesis, University of Newcastle Upon Tyne, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315592.

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