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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
21

Classic optimal control in continuous time with applications in economics

Ni, Lingfei January 1900 (has links)
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.
22

A control theoretic perspective on learning in robotics

O'Flaherty, Rowland Wilde 27 May 2016 (has links)
For robotic systems to continue to move towards ubiquity, robots need to be more autonomous. More autonomy dictates that robots need to be able to make better decisions. Control theory and machine learning are fields of robotics that focus on the decision making process. However, each of these fields implements decision making at different levels of abstraction and at different time scales. Control theory defines low-level decisions at high rates, while machine learning defines high-level decision at low rates. The objective of this research is to integrate tools from both machine leaning and control theory to solve higher dimensional, complex problems, and to optimize the decision making process. Throughout this research, multiple algorithms were created that use concepts from both control theory and machine learning, which provide new tools for robots to make better decisions. One algorithm enables a robot to learn how to optimally explore an unknown space, and autonomously decide when to explore for new information or exploit its current information. Another algorithm enables a robot to learn how to locomote with complex dynamics. These algorithms are evaluated both in simulation and on real robots. The results and analysis of these experiments are presented, which demonstrate the utility of the algorithms introduced in this work. Additionally, a new notion of “learnability” is introduced to define and determine when a given dynamical system has the ability to gain knowledge to optimize a given objective function.
23

Optimal Control of Electrified Powertrains

Sivertsson, Martin January 2015 (has links)
Vehicle powertrain electrification, i.e. combining the internal combustion engine (ICE) with an electric motor (EM), is a potential way of meeting the increased demands for efficient and low emission transportation, at a price of increased powertrain complexity since more degrees of freedom (DoF) have been introduced. Optimal control is used in a series of studies of how to best exploit the additional DoFs. In a diesel-electric powertrain the absence of a secondary energy storage and mechanical connection between the ICE and the wheels means that all electricity used by the EMs needs to be produced simultaneously by the ICE, whose rotational speed is a DoF. This in combination with the relatively slow dynamics of the turbocharger in the ICE puts high requirements on good transient control. In optimal control studies, accurate models with good extrapolation properties are needed. For this aim two nonlinear physics based models are developed and made available that fulfill these requirements, these are also smooth in the region of interest, to enable gradient based optimization techniques. Using optimal control and one of the developed models, the turbocharger dynamics are shown to have a strong impact on how to control the powertrain and neglecting these can lead to erroneous estimates both in the response of the powertrain as well as how the powertrain should be controlled. Also the objective, whether time or fuel is to be minimized, influences the engine speed-torque path to be used, even though it is shown that the time optimal solution is almost fuel optimal. To increase the freedom of the powertrain control, a small energy storage can be added to assist in the transients. This is shown to be especially useful to decrease the response time of the powertrain, but the manner it is used, depends on the time horizon of the optimal control problem. The resulting optimal control solutions are for certain cases oscillatory when stationary controls would have been expected. This is shown to be neither an artifact of the discretization used nor a result of the modeling assumptions used. Instead it is for the formulated problems actually optimal to use periodic control in certain stationary operating points. Measurements show that the pumping torque is different depending on whether the controls are periodic or constant despite the same average value. Whether this is beneficial or not depends on the operating point and control frequency, but can be predicted using optimal periodic control theory. In hybrid electric vehicles (HEV) the size of the energy storage reduces the impact of poor transient control, since the battery can compensate for the slower dynamics of the ICE. For HEVs the problem instead is how and when to use the battery to ensure good fuel economy. An adaptive map-based equivalent consumption minimization strategy controller using battery state of charge for feedback control is designed and tested in a real vehicle with good results, even when the controller is started with poor initial values. In a plug-in HEV (PHEV) the battery is even larger, enabling all-electric drive, making it it desirable to use the energy in the battery during the driving mission. A controller is designed and implemented for a PHEV Benchmark and is shown to perform well even for unknown driving cycles, requiring a minimum of future knowledge. / Elektrifiering av drivlinan i fordon är ett sätt att möta kraven på transporter med hög effektivitet och låga utsläpp. Att byta ut förbränningsmotorn mot en elmotor kan ge vinningar avseende effektivitet, prestanda och utsläpp, men till en kostnad av lägre mobilitet på grund av eletriska energilagers relativt låga energitäthet i jämförelse med fossila bränslen. Att istället komplettera förbränningsmotorn med en elmotor erbjuder möjligheten att kombinera de två systemens fördelar och samtidigt undvika nackdelarna. Att använda mer än en motor i drivlinan ökar komplexiteten eftersom fler frihetsgrader har introducerats. Detta ställer ökade krav på utformningen av reglersystemet för att få ut det mesta av potentialen i drivlinan. I optimal styrning använder man matematiska modeller och optimeringsalgoritmer för att beräkna hur man bäst styr det modellerade systemet. Storleken på det elektriska energilagret påverkar dock valet av optimal styrnings-metod samt vilken detaljnivå på modellerna som behövs. I avhandlingen används optimal styrning i en serie studier av hur man bäst utnyttjar de extra frihetsgraderna som elektrifieringen har introducerat. I en diesel-elektrisk drivlina finns det ingen mekanisk koppling mellan motorn och hjulen, likt en växellåda i ett vanligt fordon, vilket gör att dieselmotorns varvtal är en frihetsgrad som måste styras. Avsaknaden av elektriskt energilager leder också till att all elektrisk energi till elmotorn måste produceras av förbränningsmotorn exakt då den behövs. Dessa två egenskaper, i kombination med den långsamma dynamiken hos turboaggregatet, ställer detta höga krav på god transientreglering. För att studera optimal styrning krävs bra modeller med goda extrapoleringsegenskaper. Med avseende på detta utvecklas två fysik-baserade modeller som uppfyller dessa krav och dessutom är tillräckligt glatta i det relevanta arbetsområdet för att möjliggöra gradient-baserade optimeringstekniker. Med optimal styrning och en av de utvecklade modellerna visas turbons dynamik ha stor påverkan på hur drivlinan bör styras. Att försumma turbodynamiken kan leda till felaktiga uppskattningar, både av drivlinans responstid, men även hur den bör styras. Kriteriet, det vill säga om bränsle eller tidsåtgången minimeras, påverkar också vilken motorvarvtal-motormoment-väg som är optimal, även om det visas att den tidsoptimala lösningen är nästan bränsleoptimal. För att ytterligare öka frihetsgraden i drivlinan kan ett elektriskt energilager användas för att assistera i transienterna. Detta visar sig vara särskilt användbart för att minska responstiden hos drivlinan, men hur det ska använda beror på tidshorisonten på optimeringsproblemet De resulterande optimala styrsignalerna är i vissa fall oscillerande där konstanta styrsignaler förväntas. Detta visas vara vare sig en effekt av den använda diskretiseringen eller modelleringsvalen som är gjorda. Istället är det för de lösta problemen faktiskt optimalt att använda periodiska styrsignaler för vissa stationära arbetspunkter. I experiment visas att pumparbetet skiljer sig beroende på om periodiska eller konstanta styrsignaler används, även om medelvärdet är detsamma. Huruvida detta ökar effektiviteten eller inte beror på arbetspunkt och periodtid. För hybridelektriska fordon (HEV) så minskar batteriets storlek effekten av dålig transientreglering då batteriet kan användas för att kompensera för den långsamma förbränningsmotordynamiken. Istället blir problemet i huvudsak hur mycket och när batteriet ska användas för att få god bränsleekonomi. En adaptiv mapp-baserad ekvivalentförbruknings-minimerande styrlag (ECMS) med återkopplad reglering baserad på batteriets laddningsnivå, utvecklas och testas i riktigt fordon med gott resultat, även vid dålig initialisering av regulatorn. För plug-in hybrider (PHEV) är batteriet större och kan dessutom laddas från elnätet, vilket medför möjlighet till rent elektrisk drift och att det är önskvärt att använda energin i batteriet under köruppdraget. För att minska energiåtgången är det däremot ofta lönsamt att blanda energin från bränsle och batteriet kontinuerligt under köruppdraget och se till att batteriet töms lagom till slutet av köruppdraget. För att åstadkomma detta måste då även urladdningstakten bestämmas. En regulator utvecklas för att minimera energiåtgången för en PHEV, det vill säga som försöker använda lagom av batteriet så det ska räcka hela vägen, men inte längre. Denna regulator implementeras för ett referensproblem, med gott resultat även för okända körcykler, trots ett minimum av framtidskunskap.
24

Finite set control transcription for optimal control applications

Stanton, Stuart Andrew 23 October 2009 (has links)
An enhanced method in optimization rooted in direct collocation is formulated to treat the finite set optimal control problem. This is motivated by applications in which a hybrid dynamical system is subject to ordinary differential continuity constraints, but control variables are contained within finite spaces. Resulting solutions display control discontinuities as variables switch between one feasible value to another. Solutions derived are characterized as optimal switching schedules between feasible control values. The methodology allows control switches to be determined over a continuous spectrum, overcoming many of the limitations associated with discretized solutions. Implementation details are presented and several applications demonstrate the method’s utility and capability. Simple applications highlight the effectiveness of the methodology, while complicated dynamic systems showcase its relevance. A key example considers the challenges associated with libration point formations. Extensions are proposed for broader classes of hybrid systems. / text
25

Lyapunov transformations and control

Manolescu, Crina Iulia January 1997 (has links)
No description available.
26

Modelling and optimisation of hybrid dynamic processes

Avraam, Marios January 2000 (has links)
No description available.
27

Homological structure of optimal systems

Bowden, Keith G. January 1983 (has links)
Pure mathematics is often classified as continuous or discrete, that is into topology and combinatorics. Classical topology is the study of spaces in the small, modern topology or homology theory is the study of their large scale structure. The latter and its applications to General Systems Theory and implications on computer programming are the subject of our investigations. A general homology theory includes boundary and adjoint operators defined over a graded category. Singular homology theory describes the structure of high dimensional Simplicial complexes, and is the basis of Kron's tearing of electrical networks. De ~ham Cohomology Theory describes the structure of exterior differential forms used to ~nalyse distributed fields in high dimensional spaces. Likewise optimal control ~roblems can be described by abstract homology theories. Ideas from tensor theory are ~sed to identify the homological structure of Leontief's economic model as a real ~xample of an optimal control system. The common property of each of the above ~ystems is that of optimisation or equivalently the mapping of an error to zero. The ~~iterion may be a metric in space, or energy in an electrical or mechanical network ~~ system, or an abstract cost function in state space or money in an economic system ~~d is always the product of a covariant and a contravariant variable. ~e axiomatic nature of General Homology Theory depends on the definition of an ~~missable category, be it group, ring or module structure. Similarly real systems ~~e analysed in terms of mutually recursive algebras, vector, matrix or polynomial. ~~rther the group morphisms or mode operators are defined recursively. An orthogonal ~~mputer language, Algo182, is proposed which is capable of manipulating the objects ~~scribed by homological systems theory, thus alleviating the tedium and insecurity t~curred in iDtplementing computer programs to analyse engineering systems.
28

Minimizing the Probability of Ruin in Exchange Rate Markets

Chase, Tyler A. 30 April 2009 (has links)
The goal of this paper is to extend the results of Bayraktar and Young (2006) on minimizing an individual's probability of lifetime ruin; i.e. the probability that the individual goes bankrupt before dying. We consider a scenario in which the individual is allowed to invest in both a domestic bank account and a foreign bank account, with the exchange rate between the two currencies being modeled by geometric Brownian motion. Additionally, we impose the restriction that the individual is not allowed to borrow money, and assume that the individual's wealth is consumed at a constant rate. We derive formulas for the minimum probability of ruin as well as the individual's optimal investment strategy. We also give a few numerical examples to illustrate these results.
29

Modelling healthcare provision for an infectious disease using optimal control

Brown, Victoria January 2010 (has links)
The development of a vaccine against some strains of the human papillomavirus (HPV) has led to many interesting public health questions [1]. We address some of these questions in the following work. We develop a compartmental mathematical model and examine the effect of waning immunity, vaccinating individuals prior to their becoming sexually active and the current government policy of vaccinating only females [2]. We calculate parameters based on data. We consider both time-dependent and age dependent ODE models and an age- and time-dependent PDE model and compare the results. We find the “effective” R0 value, Re0, for the time-dependent models. We introduce optimal control to both the time-dependent and age-dependent ODE models to assess the most cost-effective method for introducing the vaccine into a population. We find that the duration of protection offered by the vaccine can influence whether it is possible to eradicate infection from the population. We find the critical proportion to vaccinate to eradicate the disease. We see that introducing male vaccination would lead to a greater proportion of individuals to be vaccinated if the disease is to be eradicated. The PDE model shows that the proportion of females vaccinated has a large impact on the proportion of females infected. We show that it is cost-effective to vaccinate males and females. Our results support current government policy for age of vaccination [2]. We conclude that potential waning immunity will impact the success of the vaccine. We broadly support government policy for vaccination but recommend including male vaccination to most cost-effectively eradicate the disease.
30

Algorithms for decision making

Riseth, Asbjørn Nilsen January 2018 (has links)
We investigate algorithms for different steps in the decision making process, focusing on systems where we are uncertain about the outcomes but can quantify how probable they are using random variables. Any decision one makes in such a situation leads to a distribution of outcomes and requires a way to evaluate a decision. The standard approach is to marginalise the distribution of outcomes into a single number that tries in some way to summarise the value of each decision. After selecting a marginalisation approach, mathematicians and decision makers focus their analysis on the marginalised value but ignore the distribution. We argue that we should also be investigating the implications of the chosen mathematical approach for the whole distribution of outcomes. We illustrate the effect different mathematical formulations have on the distribution with one-stage and sequential decision problems. We show that different ways to marginalise the distributions can result in very similar decisions but each way has a different complexity and computational cost. It is often computationally intractable to approximate optimal decisions to high precision and much research goes into developing algorithms that are suboptimal in the marginalised sense, but work within the computational budget available. If the performance of these algorithms is evaluated they are mainly judged based on the marginalised values, however, comparing the performance using the full distribution provides interesting information: We provide numerical examples from dynamic pricing applications where the suboptimal algorithm results in higher profit than the optimal algorithm in more than half of the realisations, which is paid for with a more significant underperformance in the remaining realisations. All the problems discussed in this thesis lead to continuous optimisation problems. We develop a new algorithm that can be used on top of existing optimisation algorithms to reduce the cost of approximating solutions. The algorithm is tested on a range of optimisation problems and is shown to be competitive with existing methods.

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