Dissertations / Theses on the topic 'Time-optimal'

Cette thèse présente trois principaux sujets de recherche, les deux premiers étant indépendants et le dernier indiquant la relation des deux premières problématiques dans un cas concret.Dans la première partie nous nous intéressons au problème de transport optimal martingale dans l’espace de Skorokhod, dont le premier but est d’étudier systématiquement la tension des plans de transport martingale. On s’intéresse tout d’abord à la semicontinuité supérieure du problème primal par rapport aux distributions marginales. En utilisant la S-topologie introduite par Jakubowski, on dérive la semicontinuité supérieure et on montre la première dualité. Nous donnons en outre deux problèmes duaux concernant la surcouverture robuste d’une option exotique, et nous établissons les dualités correspondantes, en adaptant le principe de la programmation dynamique et l’argument de discrétisation initie par Dolinsky et Soner.La deuxième partie de cette thèse traite le problème du plongement de Skorokhod optimal. On formule tout d’abord ce problème d’optimisation en termes de mesures de probabilité sur un espace élargi et ses problèmes duaux. En utilisant l’approche classique de la dualité; convexe et la théorie d’arrêt optimal, nous obtenons les résultats de dualité. Nous rapportons aussi ces résultats au transport optimal martingale dans l’espace des fonctions continues, d’où les dualités correspondantes sont dérivées pour une classe particulière de fonctions de paiement. Ensuite, on fournit une preuve alternative du principe de monotonie établi par Beiglbock, Cox et Huesmann, qui permet de caractériser les optimiseurs par leur support géométrique. Nous montrons à la fin un résultat de stabilité qui contient deux parties: la stabilité du problème d’optimisation par rapport aux marginales cibles et le lien avec un autre problème du plongement optimal.La dernière partie concerne l’application de contrôle stochastique au transport optimal martingale avec la fonction de paiement dépendant du temps local, et au plongement de Skorokhod. Pour le cas d’une marginale, nous retrouvons les optimiseurs pour les problèmes primaux et duaux via les solutions de Vallois, et montrons en conséquence l’optimalité des solutions de Vallois, ce qui regroupe le transport optimal martingale et le plongement de Skorokhod optimal. Quand au cas de deux marginales, on obtient une généralisation de la solution de Vallois. Enfin, un cas spécial de plusieurs marginales est étudié, où les temps d’arrêt donnés par Vallois sont bien ordonnés
This PhD dissertation presents three research topics, the first two being independent and the last one relating the first two issues in a concrete case.In the first part we focus on the martingale optimal transport problem on the Skorokhod space, which aims at studying systematically the tightness of martingale transport plans. Using the S-topology introduced by Jakubowski, we obtain the desired tightness which yields the upper semicontinuity of the primal problem with respect to the marginal distributions, and further the first duality. Then, we provide also two dual formulations that are related to the robust superhedging in financial mathematics, and we establish the corresponding dualities by adapting the dynamic programming principle and the discretization argument initiated by Dolinsky and Soner.The second part of this dissertation addresses the optimal Skorokhod embedding problem under finitely-many marginal constraints. We formulate first this optimization problem by means of probability measures on an enlarged space as well as its dual problems. Using the classical convex duality approach together with the optimal stopping theory, we obtain the duality results. We also relate these results to the martingale optimal transport on the space of continuous functions, where the corresponding dualities are derived for a special class of reward functions. Next, We provide an alternative proof of the monotonicity principle established in Beiglbock, Cox and Huesmann, which characterizes the optimizers by their geometric support. Finally, we show a stability result that is twofold: the stability of the optimization problem with respect to target marginals and the relation with another optimal embedding problem.The last part concerns the application of stochastic control to the martingale optimal transport with a payoff depending on the local time, and the Skorokhod embedding problem. For the one-marginal case, we recover the optimizers for both primal and dual problems through Vallois' solutions, and show further the optimality of Vallois' solutions, which relates the martingale optimal transport and the optimal Skorokhod embedding. As for the two-marginal case, we obtain a generalization of Vallois' solution. Finally, a special multi-marginal case is studied, where the stopping times given by Vallois are well ordered

A payment is the most fundamental aspect of a trade that involves funds. In recent years, the development of new payment services has accelerated significantly as the world has moved further into the digital era. This transition has led to an increased demand of digital payment solutions that can handle trades across the world. As trades today can be agreed at any time wherever the payer and payee are located, the party that mediates payments must at any time to be available in order to mediate an agreed exchange. This requires the payment service provider to always have funds available in the required countries and currencies in order for trades to always be available. This thesis concerns how a payment service provider can reallocate capital in a cost efficient way in order for trades to always be available. Traditionally, the reallocation of capital is done in a rule-based manner, which discard the cost dimension and thereby only focus on the reallocation itself. This thesis concerns methods to optimally reallocate capital focusing on the cost of transferring capital within the network. Where the concerned methods has the potential of transferring capital in a far more cost efficient way. When mathematically formulating the reallocation decisions as an optimization problem, the cost function is formulated as a linear program with both Boolean and real constraints. This impose non-feasibility of locating the optimal solution using traditional methods for linear programs, why developed traditional and more advanced methods were used. The model was evaluated based on a large number of simulations in comparison with the performance of a rule-based reallocation system. The developed model provides a significant cost reduction compared to the rule-based approach and thereby outperforms the traditional reallocation system. Future work should focus on expanding the model by broadening the available transfer options, by increasing the considered uncertainty via a bayesian treatment and finally by considering all cost aspects of the network.
En betalning är den mest fundamentala aspekten av handel som involverar kapital. De senaste åren har utvecklingen av nya betalmedel ökat drastiskt då världen fortsatt att utvecklas genom digitaliseringen. Utvecklingen har lett till en ökad efterfrågan på digitala betalningslösningar som kan hantera handel över hela världen. Då handel idag kan ske när som helst oberoende av var betalaren och betalningsmottagaren befinner sig, måste systemet som genomför betalningen alltid vara tillgängligt för att kunna förmedla handel mellan olika parter. Detta kräver att betalningssystemet alltid måste ha medel tillgängligt i efterfrågade länder och valutor för att handeln ska kunna genomföras. Den här uppsatsen fokuserar på hur kapital kostnadseffektivt kan omallokeras i ett betalsystem för att säkerställa att handel alltid är tillgängligt. Traditionellt har omallokeringen av kapital gjorts på ett regelbaserat sätt, vilket inte tagit hänsyn till kostnadsdimensionen och därigenom enbart fokuserat på själva omallokeringen. Den här uppsatsen använder metoder för att optimalt omallokera kapital baserat på kostnaderna för omallokeringen. Därigenom skapas en möjlighet att flytta kapital på ett avsevärt mer kostnadseffektivt sätt. När omallokeringsbesluten formuleras matematiskt som ett optimeringsproblem är kostnadsfunktionen formulerad som ett linjärt program med både Booleska och reella begränsningar av variablerna. Detta gör att traditionella lösningsmetoder för linjära program inte är användningsbara för att finna den optimala lösningen, varför vidareutveckling av tradtionella metoder tillsammans med mer avancerade metoder använts. Modellen utvärderades baserat på ett stort antal simuleringar som jämförde dess prestanda med det regelbaserade systemet. Den utvecklade modellen presterar en signfikant kostnadsreduktion i jämförelse med det regelbaserade systemet och överträffar därigenom det traditionellt använda systemet. Framtida arbete bör fokusera på att expandera modellen genom att utöka de potentiella överföringsmöjligheterna, att ta ökad hänsyn till osäkerhet genom en bayesiansk hantering, samt slutligen att integrera samtliga kostnadsaspekter i nätverket.

There are many situations in which one can preview future reference signals, or future disturbances. Optimal Preview Control is concerned with designing controllers which use this preview to improve closed-loop performance. In this thesis a general preview control problem is presented which includes previewable disturbances, dynamic weighting functions, output feedback and nonpreviewable disturbances. It is then shown how a variety of problems may be cast as special cases of this general problem; of particular interest is the robust preview tracking problem and the problem of disturbance rejection with uncertainty in the previewed signal. The general preview problem is solved in both the Fh and Beo settings. The H2 solution is a relatively straightforward extension ofpreviously known results, however, our contribution is to provide a single framework that may be used as a reference work when tackling a variety of preview problems. We also provide some new analysis concerning the maximum possible reduction in closed-loop H2 norm which accrues from the addition of preview action. The solution to the Hoo problem involves a completely new approach to Hoo preview control, in which the structure of the associated Riccati equation is exploited in order to find an efficient algorithm for computing the optimal controller. The problem tackled here is also more generic than those previously appearing in the literature. The above theory finds obvious applications in the design of controllers for autonomous vehicles, however, a particular class of nonlinearities found in typical vehicle models presents additional problems. The final chapters are concerned with a generic framework for implementing vehicle preview controllers, and also a'case study on preview control of a bicycle.

The most popular and fundamental portfolio optimization problem is Markowitz'
s one period mean-variance portfolio selection problem. However, it is criticized because of its one period static nature. Further, the estimation of the stock price expected return is a particularly hard problem. For this purpose, there are a lot of studies solving the mean-variance portfolio optimization problem in continuous time. To solve the estimation problem of the stock price expected return, in 1992, Black and Litterman proposed the Bayesian asset allocation method in discrete time. Later on, Lindberg has introduced a new way of parameterizing the price dynamics in the standard Black-Scholes and solved the continuous time mean-variance portfolio optimization problem. In this thesis, firstly we take up the Lindberg'
s approach, we generalize the results to a jump-diffusion market setting and we correct the proof of the main result. Further, we demonstrate the implications of the Lindberg parameterization for the stock price drift vector in different market settings, we analyze the dependence of the optimal portfolio from jump and diffusion risk, and we indicate how to use the method. Secondly, we present the Lagrangian function approach of Korn and Trautmann and we derive some new results for this approach, in particular explicit representations for the optimal portfolio process. In addition, we present the L2-projection approach of Schweizer for the continuous time mean-variance portfolio optimization problem and derive the optimal portfolio and the optimal wealth processes for this approach. While, deriving these results as the underlying model, the market parameterization of Lindberg is chosen. Lastly, we compare these three different optimization frameworks in detail and their attractive and not so attractive features are highlighted by numerical examples.

The time optimal slewing problem for flexible spacecraft is considered. We study single-axis rotational maneuvers for a simple flexible system, consisting of a rigid hub with an elastic appendage. The equations of motions are derived by Hamilton’s Principle, and a discrete nonlinear model is obtained by the assumed modes method. The problem is first solved in a discrete linearized space by parameter optimization. Optimality is verified by Pontryagin’s Maximum Principle. The linear solutions are then used to obtain time optimal solutions for the non-linear problem by a multiple-shooting algorithm. Although this approach is applicable to arbitrary boundary conditions, this work is confined, almost exclusively, to rest-to-rest maneuvers. These maneuvers are shown to possess some interesting symmetric and asymptotic properties. The problem is further analyzed in infinite-dimensional space, and the convergence of the finite-dimensional approximations is studied. Finally, a soft version of the time optimal slewing problem is considered, where the control is bounded only by a penalty term in the cost functional. A perturbation technique is applied to further simplify this problem.
Ph. D.

 The goal of this thesis is to study the economics of computational learning. Attention is also paid to applications of computational learning models, especially Valiant's so-called `probably approximately correctly' (PAC) learning model, in econometric situations.

Specifically, an economically reasonable stopping time model of learning is the subject of two attached papers. In the rst paper, Paper A, the economics of PAC learning are considered. It is shown how a general form of the optimal stopping time bounds can be achieved using the PAC convergence rates for a `pessimistic-rational' learner in the most standard binary case of passive supervised PAC model of finite Vapnik-Chervonenkis (VC) dimension.

 

The second paper, Paper B, states precisely and improves the ideas introduced in Paper A and tests them in a specific and mathematically simple case. Using the maxmin procedure of Gilboa and Schmeidler the bounds for the stopping time are expressed in terms of the largest expected error of recall, and thus, effectively, in terms of the least expected reward. The problem of locating a real number θ by testing whether x_i ≤ θ , with x_i drawn from an calculated for a range of term rates, sample costs and rewards/penalties from a recall ae included. The standard econometric situations, such as product promotion, market research, credit risk assessment, and bargaining and tenders, where such bounds could be of interest, are pointed. 

These two papers are the essence of this thesis, and form it togheter with an introduction to the subject of learning.

Målet med denna avhandling är att studera optimering av inlärning när det finns kostnader. Speciellt studerar jag Valiants så kallade PAC-inlärningsmodell  (Probably Approximately Correctly), ofta använd inom datavetenskap. I två artiklar behandlar jag hur länge, ur ekonomisk synvinkel, inlärningsperioden bör fortsätta.

I den första artikeln visar vi hur en generell form av begränsningar av den optimala inlärningsperioden kan fås med hjälp av PAC-konvergenshastigheten för en ’pessimistiskt rationell’ studerande (i det vanligaste binära fallet av passiv PAC-inlärningsmodell med ändlig VC-dimension).

I den andra artikeln fördjupar och förbättrar vi idéerna från den första artikeln, och testar dem i en specifik situation som är matematiskt enkel. Med hjälp av Gilboa – Schmeidlers max - minprocedur  uttrycker vi begränsningarna av den optimala inlärningsperioden som funktion av det största förväntade felet och därmed som funktion av den minsta förväntade belöningen. Vi diskuterar problemet med att hitta ett reellt tal θ genom testning av huruvida x_i ≤ θ, där x_i dras från en okänd fördelning. Här tar vi också upp exempel på begränsningar av inlärningsperioden, beräknade för en mängd av diskontovärden, stickprovskostnader och belöning/straff för erinran, samt en del vanliga ekonometriska situationer där sådana begränsningar är av intresse, såsom marknadsföring av produkter, marknadsanalys, kreditriskskattning och offertförhandling.

Avhandlingen består i huvuddel av dessa två artiklar samt en kort introduktion till ekonomiska, matematiska och datavetenskapliga inlärningsmodeller.

 

Real-Time Bidding (RTB) is revolutionising display advertising by facilitating a real-time auction for each ad impression. As they are able to use impression-level data, such as user cookies and context information, advertisers can adaptively bid for each ad impression. Therefore, it is important that an advertiser designs an effective bidding strategy which can be abstracted as a function - mapping from the information of a specific ad impression to the bid price. Exactly how this bidding function should be designed is a non-trivial problem. It is a problem which involves multiple factors, such as the campaign-specific key performance indicator (KPI), the campaign lifetime auction volume and the budget. This thesis is focused on the design of automatic solutions to this problem of creating optimised bidding strategies for RTB auctions: strategies which are optimal, that is, from the perspective of an advertiser agent - to maximise the campaign's KPI in relation to the constraints of the auction volume and the budget. The problem is mathematically formulated as a functional optimisation framework where the optimal bidding function can be derived without any functional form restriction. Beyond single-campaign bid optimisation, the proposed framework can be extended to multi-campaign cases, where a portfolio-optimisation solution of auction volume reallocation is performed to maximise the overall profit with a controlled risk. On the model learning side, an unbiased learning scheme is proposed to address the data bias problem resulting from the ad auction selection, where we derive a "bid-aware'' gradient descent algorithm to train unbiased models. Moreover, the robustness of achieving the expected KPIs in a dynamic RTB market is solved with a feedback control mechanism for bid adjustment. To support the theoretic derivations, extensive experiments are carried out based on large-scale real-world data. The proposed solutions have been deployed in three commercial RTB systems in China and the United States. The online A/B tests have demonstrated substantial improvement of the proposed solutions over strong baselines.

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
Includes bibliographical references (p. 108-109).
by Sudhanshu Madan Aggarwal.
M.S.

The purpose of this research is to develop an optimal kernel which would be used in a real-time engineering and communications system. Since the application is a real-time system, relevant real-time issues are studied in conjunction with kernel related issues. The emphasis of the research is the development of a kernel which would not only adhere to the criteria of a real-time environment, namely determinism and performance, but also provide the flexibility and portability associated with non-real-time environments. The essence of the research is to study how the features found in non-real-time systems could be applied to the real-time system in order to generate an optimal kernel which would provide flexibility and architecture independence while maintaining the performance needed by most of the engineering applications. Traditionally, development of real-time kernels has been done using assembly language. By utilizing the powerful constructs of the C language, a real-time kernel was developed which addressed the goals of flexibility and portability while still meeting the real-time criteria. The implementation of the kernel is carried out using the powerful 68010/20/30/40 microprocessor based systems.

Continuous-time (CT) SD modulators are growing increasingly popular in wideband A/D conversion. Such applications require high orders of quantisation noise shaping and multi-bit quantisers, to compensate for the resulting low oversampling ratios. These, however, add circuit complexities and excess loop delay that are detrimental to the modulator control loop. A CT SD modulator can potentially achieve a higher performance with a lower bandwidth requirement than its discrete-time (DT) counterpart. Unfortunately, CT SD modulators suffer from problems not seen in dependent jitter and non-rectangular DAC pulse shapes. Low-oversampling CT SD modulators are also sensitive to a low bandwidth in the input stage of the forward filter. These effects are often tackled by a modification ion the CT SD modulator architecture. Unfortunately, the resulting CT SD modulator control loop is often suboptimal and sensitive to changes in the modulator coefficients. In this thesis, a design-by-optimisation method is proposed to find the optimum that satisfies the constraints set by the implementation of the CT SD modulator, its feasibility and any other additional design criteria. Robustness in the final design is ensured by optimising directly on the coefficients of the CT SD modulator, and evaluating the stability and the performance of its DT equivalent model. The DT equivalent is computed using a numerical implementation of the impulse-invariance technique. This implementation can deal with both excess loop delay and non-rectangular DAC pulse shapes, numerically and in general form. This is, to the best of the author’s knowledge, the first implementation of its kind. It is shown that for a low value of loop delay, a resonator based forward filter is optimum, while, contrary to assumptions made in the literature, real poles in the forward filter are preferable for moderate values of loop delay. It is hoped that the bandwidth requirement of CT modulators can be minimised in a similar manner. A numerical curve fitting approach is also presented that models many of the nonidealities in an integrator circuit response with a low-order model transfer function.

This work focuses on control and trajectory optimization strategies for high speed contouring of machine tools. In the first part, control strategies are studied. Studied strategies are divided into three major categories. Axial error controllers, contour error controllers, and feed forward controllers. The control strategies are benchmarked on a biaxial XY table. The least contouring error was recorded for the control structure consisting of Cartesian Servo Control (CSC) with a Proportional Derivative Integral (PID) regulator + Torque Feed Forward (TFF). As for the trajectory optimization, a new real time algorithm to select time-optimal feedrates has been proposed. The algorithm is independent of the spline representation of the nominal path, and incorporates both velocity and acceleration constraints. The fact that the proposed algorithm is independent from the spline representation (since it simply adjusts sampling times for position increments), makes it more flexible than conventional algorithms in the literature that require particular spline representations of the reference trajectory. Also the proposed algorithm is computationally efficient because: 1) an analytical solution to the optimization is applied at every time step rather than a global numerical optimization procedure, and 2) other analytical solutions in the literature require a forward and a backward pass over the compete trajectory. The new algorithm only backtracks over a short window before decelerations. Finally, this study also introduces two new reference path generation techniques that use part tolerance values to reduce machining time.
Applied Science, Faculty of
Engineering, School of (Okanagan)
Graduate

Esta tesis tiene cuatro capítulos que exploran el papel de la deuda pública en el problema de la inconsistencia temporal de la política fiscal óptimal. El Capítulo 1 resume la literatura existente en el área de inconsistencia temporal, señala las principales limitaciones de dicha literatura y pone en contexto las cuestiones que esta tesis ha pretendido responder. El Capítulo 2 analiza la composición óptima de la deuda en economías con un mecanismo de reputación. En economías sin un mecanismo de reputación, el principal resultado de la literatura es que se necesitan de estructuras de deuda muy ricas con el fin de resolver el problema de la inconsistencia temporal. Nosotros consideramos una economía con un mecanismo de reputación y encotramos que el enriquecimiento de la estructura de la deuda aumenta el coste de mantener la reputación y puede hacer a la política óptima inconsistente en el tiempo. El Capítulo 3 estudia las propiedades de los impuestos óptimos consistentes en el tiempo para economías con un mercado de deuda pública. El principal resultado para economías sin deuda pública es que el impuesto óptimo sobre el capital es distinto de cero en el estado estacionario. Nosotros consideramos una economía con deuda pública y obtenemos que el impuesto óptimo sobre el capital es cero. En consecuencia, la deuda pública es un instrumento primordial para resolver los problemas de inconsistencia temporal. Finalmente, el Capítulo 4 estudia el papel de la restructuración de la deuda en el problema de la inconsistencia temporal para economías con un stock the capital privado y crecimiento endógeno a través del capital público. El resultado general de la literatura es que el método de la restructuración de la deuda no puede resolver el problema de la inconsistencia temporal en economías con capital privado. Este problema ha llevado a utilizar este método en economías muy simples que no tienen capital ni, por ejemplo, crecimiento. Nosostros consideramos una economía con capital privado y crecimiento endógeno. En este contexto, nosotros construimos las condiciones necesarias para resolver el problema de la inconsistencia y, además, caracterizar las propiedades distintivas de la restructuración de la deuda en este nuevo contexto. En resumen, esta tesis ha intentado y, de hecho, ha respondido a importantes preguntas que permanecían sin respuesta en la literatura de inconsistencia-temporal de la política fiscal óptima.
This dissertation contains four chapters exploring the role of debt in the time-inconsistency problem of optimal fiscal policy. Chapter 1 reviews the existing literature on the time-inconsistency problem, highlights the main short-commings of this literature and introduces the main questions that this thesis aims to answer. Chapter 2 analyzes the optimal management of the composition of debt under a reputation mechanism. In economies without a reputation mechanism, the main result of the literature is that very rich debt structures are required to solve the time-inconsistency problem. We consider an economy with a reputation mechanism and we find that an enrichment of the debt structure increases the costs of maintaining the reputation and, thus, it can make the optimal policy time-inconsistent. Chapter 3 studies the properties of the optimal time-consistent taxes for an economy with public debt. The existing literature has studied the properties of the optimal taxes without commitment for economies without a market for public debt. The main result for economies without public debt was that the optimal capital tax rate is different from zero at the steady state. We consider an economy with public debt and we obtain that the optimal capital tax rate turns out to be zero. Therefore, public debt is again a central commitment device against deviation from the announced policy. Finally, Chapter 4 studies the role of debt restructuring in the time-inconsistency problem of optimal fiscal policy for an economy with private capital and endogenous growth achieved via public capital. A general result of the previous literature is that the debt restructuring method cannot make the optimal policy time-consistent in the presence of the capital levy problem. This problem has been widely recognized and it has limited the debt restructuring method to models with no private capital and no growth. We consider an economy with private capital and endogenous growth. In this context, we build conditions to solve the time-inconsistency problem and, moreover, we characterize the distinctive properties of debt restructuring in this environment. Summing up, this thesis answers important questions that remained unanswered in the literature of time-inconsistency of optimal fiscal policy.

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Egerstedt, Magnus; Committee Co-Chair: Wardi, Yorai; Committee Member: Riley, George; Committee Member: Taylor, David; Committee Member: Tovey, Craig; Committee Member: Yezzi, Anthony. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Astronautical Engineer and M.S. in Astronautical Engineering)--Naval Postgraduate School, June 2008.
Thesis Advisor(s): Ross, I. Michael. "December 2004." Description based on title screen as viewed on September 30, 2008. Includes bibliographical references. Also available in print.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2001.
Includes bibliographical references (p. 113-116).
Product and manufacturing system design are the core issues in product development and dominate the profitability of a company. In order to assess and optimize the product and manufacturing system design, an objective evaluation framework is needed. Despite the many existing tools for product and manufacturing system design, there is a missing link between the product design and the production performances under system variability. The goal of the thesis is to explore and understand the interactions among part design and tolerancing, processes and system variability, and system control decision, then provide an integrated model to assess the total cost in a system. This model will be used to aid part design, tolerancing, batching, as well as strategy analysis in process improvement. A two-stage modeling approach is used to tackle the problem: quality prediction and production prediction. The quality prediction model projects the process variations into the output quality variations at each manufacturing stage, then predict the yield rate from the stochastic behavior of the variations and the tolerance. The production prediction model projects the demand rate and variability, processing times and variability, yield rates and batch-sizes into the manufacturing cycle time and inventories. After the performances are predicted through the previous two models, concurrent optimization of part design, tolerance, and batch-sizes are achieved by varying them to find the minimum cost. A case study at Boeing Tube shop is used to illustrate this approach. The result shows that the costless decisions in part design, tolerancing, and batch- sizes can significantly improve the system performance. In addition, conducting them separately or without using the system performance as the evaluation criteria may only lead to the local optima.
by Yu-Feng Wei.
Ph.D.

The study of cycles in the context of economic time series has been active for many decades, if not centuries; however, it was only in recent decades that more formal approaches for identifying cycles have been developed. Litvine and Bismans (2015) proposed a new approach for dating cycles in financial time series, for purposes of optimising buysell strategies. In this approach, cycle dating is presented as an optimisation problem. They also introduced a method for optimising this problem, known as the hierarchical method (using full evaluation 2, or HR-FE2). However, this method may be impractical for large data sets as it may require unacceptably long computation time. In this study, new procedures that date cycles using the approach proposed by Litvine and Bismans (2015), were introduced, and were speciffically developed to be feasible for large time series data sets. These procedures are the stochastic generation and adaptation (SGA), buy-sell adapted Extrema importance identity sequence retrieval (BSA-EIISR) and buysell adapted bottom-up (BSA-BU) methods. An existing optimisation technique, known as particle swarm optimisation (PSO), was also employed. A statistical comparison was then made between these methods, including HR-FE2. This involved evaluating, on simulated data, the performance of the algorithms in terms of objective function value and computation time on different time series lengths, Hurst exponent, and number of buy-sell points. The SRace methodology (T. Zhang, Georgiopoulos, and Anagnostopoulos 2013) was then applied to these results in order to determine the most effcient methods. It was determined that, statistically, SGA, BSA-EIISR and BSA-BU are the most effcient methods. Number of buysell points was found to have the largest effect on relative performance of these methods. In some cases, the Hurst exponent also has a small effect on relative performance.

This thesis investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. Although the system optimal assignment is not a realistic representation of traffic, it provides a bound on performance and shows how the transport planner or engineer can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. The analysis shows that to operate the transport system optimally, each traveller in the system should consider the dynamic externality that he or she imposes on the system from the time of his or her entry. To capture this dynamic externality, we develop a novel sensitivity analysis of travel cost. Solution algorithms are developed to calculate the dynamic externality and traffic assignments based on the analyses. We also investigate alternative solution strategies and the effect of time discretization on the quality of calculated assignments. Numerical examples are given and the characteristics of the results are discussed. Calculating dynamic system optimal assignment and the associated optimal toll could be too difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered in this thesis include both uniform and congestion-based tolling strategies, which are compared with the dynamic system optimal toll so that their performance can be evaluated. In deriving the tolling strategies, it is assumed that we have an exact model for the underlying traffic behaviour. In reality, we do not have such information so that the robustness of a toll calculation method is an important issue to be investigated in practice. It is found that the tolls calculated by using divided linear traffic models can perform well over a wide range of scenarios. The divided linear travel time models thus should receive more attention in the future research on robust dynamic traffic control strategies design. In conclusion, this thesis contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.

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This thesis considers the problem of time-optimal spacecraft slew maneuvers. Since the work of Bilimoria and Wie it has been known that the time-optimal reorientation of a symmetric rigid body was not the eigenaxis maneuver once thought to be correct. Here, this concept is extended to axisymmetric and asymmetric rigid body reorientations with idealized independent torque generating devices. The premise that the time-optimal maneuver is not, in general, an eigenaxis maneuver, is shown to hold for all spacecraft configurations. The methodology is then extended to include spacecraft control systems employing magnetic torque rods, a combination of pitch bias wheel with magnetic torque rods, and finally to control systems employing single gimbal control moment gyros. The resulting control solutions, designed within the limitations of the actuators, eliminate the requirement to avoid actuator singularities. Finally, by employing sampled-state feedback the viability of real-time optimal closed loop control is demonstrated.

Specifically, we are interested in the question of whether or not the supposed superiority of 'time inconsistent' policies vis-a-vis 'consistent' ones is correct. Given that the notion of 'inconsistency' forms the basis for the recent arguments in favour of 'rules' and against the use of control techniques, this question is of obvious importance. Briefly, the structure of the thesis is as follows. The first chapter concentrates on specifying the general nature of the problems tackled in the 'time inconsistency' literature, and forms the framework for the analysis which follows. Seminal papers on the issue of the 'inconsistency' of optimal plans and the inferiority of 'consistent' solutions are then examined in chapters two and three. A synthesis of the literature is reviewed in chapter four. Chapter five stands by itself as an illustration of the logical difficulties underlying claims that 'optimal' policies are in general 'time inconsistent'. The conclusion is in chapter six. Bibliography: pages 49-51.

Optimal control problems (OCPs) governed by convection dominated diffusion-convection-reaction equations arise in many science and engineering applications such as shape optimization of the technological devices, identification of parameters in environmental processes and flow control problems. A characteristic feature of convection dominated optimization problems is the presence of sharp layers. In this case, the Galerkin finite element method performs poorly and leads to oscillatory solutions. Hence, these problems require stabilization techniques to resolve boundary and interior layers accurately. The Streamline Upwind Petrov-Galerkin (SUPG) method is one of the most popular stabilization technique for solving convection dominated OCPs. The focus of this thesis is the application and analysis of the SUPG method for distributed and boundary OCPs governed by evolutionary diffusion-convection-reaction equations. There are two approaches for solving these problems: optimize-then-discretize and discretize-then-optimize. For the optimize-then-discretize method, the time-dependent OCPs is transformed to a biharmonic equation, where space and time are treated equally. The resulting optimality system is solved by the finite element package COMSOL. For the discretize-then-optimize approach, we have used the so called allv at-once method, where the fully discrete optimality system is solved as a saddle point problem at once for all time steps. A priori error bounds are derived for the state, adjoint, and controls by applying linear finite element discretization with SUPG method in space and using backward Euler, Crank- Nicolson and semi-implicit methods in time. The stabilization parameter is chosen for the convection dominated problem so that the error bounds are balanced to obtain L2 error estimates. Numerical examples with and without control constraints for distributed and boundary control problems confirm the effectiveness of both approaches and confirm a priori error estimates for the discretize-then-optimize approach.

This work is a research on the minimum time vehicle manoeuvring problem, with a particular application to finding the minimum lap time for a Formula One racing car. The proposed method allows to solve the general problem of evaluating the vehicle lateral and longitudinal controls which yield the minimum time required to traverse a lap of a circuit. The minimum time vehicle manoeuvring problem is formulated as one of Optimal Control and is solved using mathematical programming methods. Novel techniques are employed to solve the resulting non-linear programming problem which allow to achieve effective optimisation with satisfactory accuracy, robustness and computational efficiency. Particularly, the proposed solution strategy is generally applicable to any arbitrarily complex vehicle mathematical model. Car and circuit models are set up, and the optimisation program is applied to investigate the sensitivity of the vehicle performance with respect to vehicle design parameters, such as the yaw moment of inertia, the total mass and the weight distribution. Furthermore, the minimum time manoeuvring problem is solved for very different vehicle configurations. The optimisation program accurately quantifies the vehicle performance in terms of manoeuvre time, and the nature of the optimal solution is shown to be always in excellent agreement with the dynamic properties of the vehicle model. A part of the work is devoted to the development of a strategy to obtain an initial estimate of the racing line and of the vehicle lateral and longitudinal controls to be used at the start of the optimisation. Two algorithms to compute the racing line using on board measured data from the real car are presented. A new mathematical model for the vehicle steering control is derived. The model uses multiple preview information of the intended path. Its structure derives from linear optimal preview control theory, but it is adapted to deal with non-linear vehicle operations arising from the inevitable tyre force saturation in vigorous manoeuvring. The excellent path following capability of the model is demonstrated by solving various path following tasks involving moderate manoeuvring and racing speeds.

Sensor networks consist of a set of wireless sensor nodes which sense the environment and route the sensed information to a sink node. Data gathering is one of the important applications in sensor networks. In this thesis, using multiple channels, we consider TDMA schedule algorithm focusing on many-to-one communication which is called convergecast. In convergecast, a packet generated in each sensor node is delivered to a sink node without any data aggregation in the intermediate node. In large network environment with many hops, we found that usage of multiple channels significantly improves delay efficiency comparing to usage of a single channel. We formulate this problem and propose heuristic algorithms for proper channel assignment and convergecast in different topologies. In general topology, with 2 channels, we present the convergecast algorithm requiring timeslot at most 2N−1+d where N is the number of sensor nodes and d is the delay to avoid interference among sensor nodes. We also found that, for general topology, usage of 4 channels contributes to even more delay efficiency which can achieve d=0. Furthermore, unlike using 3 or fewer channels, using 4 channels is also memory efficient without creating an extra internal memory table in a sensor node to avoid interference among nodes. Additionally, such delay efficiency can result in energy efficiency which is also another important issue in sensor networks.
Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science.

Inverse optimal control is the problem of computing a cost function with respect to which observed state input trajectories are optimal. We present a new method of inverse optimal control based on minimizing the extent to which observed trajectories violate first-order necessary conditions for optimality. We consider continuous-time deterministic optimal control systems with a cost function that is a linear combination of known basis functions. We compare our approach with three prior methods of inverse optimal control. We demonstrate the performance of these methods by performing simulation experiments using a collection of nominal system models. We compare the robustness of these methods by analyzing how they perform under perturbations to the system. We consider two scenarios: one in which we exactly know the set of basis functions in the cost function, and another in which the true cost function contains an unknown perturbation. Results from simulation experiments show that our new method is computationally efficient relative to prior methods, performs similarly to prior approaches under large perturbations to the system, and better learns the true cost function under small perturbations. We then apply our method to three problems of interest in robotics. First, we apply inverse optimal control to learn the physical properties of an elastic rod. Second, we apply inverse optimal control to learn models of human walking paths. These models of human locomotion enable automation of mobile robots moving in a shared space with humans, and enable motion prediction of walking humans given partial trajectory observations. Finally, we apply inverse optimal control to develop a new method of learning from demonstration for quadrotor dynamic maneuvering. We compare and contrast our method with an existing state-of-the-art solution based on minimum-time optimal control, and show that our method can generalize to novel tasks and reject environmental disturbances.

There is currently a gap in translating the performance enhancements made possible by new maneuver strategies into operational benefits derived for spacecraft missions. In the context of imaging satellites, slew time is one of the key factors that influences the economic performance of image collection operations. To analyze the operational benefits associated with adopting time-optimal maneuver strategies to reduce slew times, this thesis studies two different operational scenarios based on the Singapore-developed X-SAT imaging spacecraft. The analysis is facilitated through the use of AGIs Systems Tool Kit (STK) software. An Analytic Hierarchy Process (AHP)-based framework is proposed to evaluate, from a business analytic point of view, the impact of incorporating time-optimal maneuvers as part of X-SAT imaging operations. The business case analysis is focused on assessing key performance indicators such as image collection volume, collected image resolution and economic revenue. The findings presented herein suggest that time-optimal maneuvers can enhance the value of imaging operations and provide additional revenue for satellite operators. Moreover, the proposed AHP hierarchy model was found to provide a convenient and methodical means for quantifying the operational advantages and economic Return on Investment (ROI) that can be obtained when incorporating new maneuver strategies into spacecraft operations.

Nowadays the industrial world has a common goal to build environment-friendly transportation and power-train systems. The first step for this aim is electrification of vehicles on the road which has remarkable influence on energy dependency and greenhouse gas emissions. Besides the first aspect the second most important factor is automation of driving technology. Self-driving technology is a significant sight for the industry to develop quality and reduce operation costs. These highlighted tendencies cooperate to enhance the sustainability along with intelligence of the modern transportation world. VERA is Volvo’s concept for driverless, electric truck technology. It holds the following tremendous advantages: automation, connectivity and electromobility – to accomplish optimal flows in transportation and logistics operations. The control is managed by autonomous electric vehicles equipped with refined systems for autonomous driving. Each vehicle is connected to a control centre. The transport control centre continuously regulates the progress of the transport and keeps an accurate supervision of each vehicle’s position, load content, the batteries’ charge and a number of other parameters. Despite the improvements performed to refine this technology, heavy batteries, long time charging and the cost of vehicle itself limit the wide usage of electric AV for long distances. The research of this paper illustrates one of the most substantial aspects in autonomous electrified driving which is the charging decision. There are several approaches used to solve this question. It is popular among contributions to provide a data-driven method, i.e by considering constraints from personal daily trips and existing charging infrastructure. As a solution, stochastic energy consumption models are designed within proposed dynamic and multi-stage optimization problems. This paper provides treatment through evaluation and optimization of expenditures for AV involved in a certain road trip.
Numera har världens industri ett gemensamt mål att bygga miljövänliga transport- och drivlinesystem. Det första steget för att nå detta mål är elektrifiering av fordon på väg, vilket har anmärkningsvärt stort inflytande på energiberoende och växthusgasutsläpp. Förutom detta är nästa viktiga steg automation av fordonsframförande. Självkörande teknik är en viktig pusselbit för industrin att utveckla kvalitet och minska driftskostnaderna. Dessa tydliga trender samverkar i intelligenta system för att förbättra hållbarheten i den moderna transportvärlden. VERA är Volvos koncept för förarlösa eldrivna transportfordon. VERA utnyttjar de stora fördelarna med automation, uppkoppling och elektromobilitet för att uppnå optimala flöden inom transport och logistik. Varje fordon är anslutet till ett kontrollcenter. Transportkontrollcentralen reglerar kontinuerligt transportens fortskridande och övervakar noggrant varje fordonets position, lastinnehåll, batteriernas laddnivå och ett antal andra parametrar. Trots att de förbättringar som gjorts för att förfina denna teknik, begränsas den breda användningen av elektriska automatiserade fordon för långa avstånd p g a tunga batterier, att laddning lång tid och kostnaden för fordonet. Undersökningen i detta kommer in på en av de mest väsentliga aspekterna i autonom elektrifierad körning som är laddningsbeslut. Syftet med detta examensarbete är att utveckla en strategi för att optimera ett godsflöde från punkt A till punkt B för medelst elekrifierade självkörande lastfordonskombinationer. Målet uppnås genom minimering av energi- och driftskostnad med den mest optimala strategin för körning och laddning. För att hitta ett optimalt köralternativ behöver man också en fordonsmodell som beskriver fordonets beteende i förhållande till färdprofil, höjd, hastighet, acceleration, massa tillsammans med drivlinedata och vissa tidsramar i transportprocessen som anses vara begränsningar för optimeringsproblem. Ett resultat var att energikostnadsvärdena visade sig vara små jämfört med driftskostnaderna. Följaktligen inriktades arbetet på tidskostnadsoptimering för att erhålla önskat transportflöde och lägsta driftkostnad med beaktande av stokastisk störning orsakad av andra fordon.

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Neste trabalho de doutorado, propõe-se RUN (Redução para Uniprocessor), um novo algoritmo de escalonamento para conjunto de tarefas periódicas com deadlines implícitas em sistemas multiprocessador de tempo real, nos quais as tarefas possuem restrições tanto no domínio do tempo quanto no domínio de valores. RUN apresenta as seguintes propriedades relevantes: - RUN é ótimo no sentido que ele produz um escalonamento correto, no qual todas as restrições temporais são atendidas, de qualquer sistemas de tarefas utilizando até 100% dos processadores da plataforma de tempo real; - RUN usa o conceito-chave do escalonamento do tempo ócio, chamado de escalonamento por dualidade, segundo o qual, em algum instante t, o escalonamento de uma tarefa utiliza tanto o conhecimento de seu tempo de execução restante, bem como o seu tempo ócio restante; - RUN baseia-se na diminuição do número de tarefas a ser escalonadas pela suas agregações em supertasks, os quais chamamos de servidores, com taxa acumulada não superior a 1. Cada servidor é responsável por escalonar o seu conjunto de tarefas clientes, de acordo com alguma política de escalonamento; - RUN utiliza o princípio original de justiça global (Gfair), de acordo com o qual cada servidor de um conjunto de tarefas T é garantido de executar por um tempo proporcional à taxa acumulada das tarefas de T entre cada duas deadlines das tarefas de T; - RUN reduz o problema do escalonamento de um conjunto de tarefas em/m/ processadores no problema equivalente do escalonamento de um ou mais conjuntos de tarefas diferentes em sistemas monoprocessador; - RUN supera significativamente os algoritmos ótimos existentes em termos de preempções com um limite superior de O(log m) preempções média por jobs em/m/ processadores.
Salvador

Thesis: S.M., Massachusetts Institute of Technology, Center for Computational Science & Engineering, February, 2021
Cataloged from the official PDF version of thesis.
Includes bibliographical references (pages 55-61).
We develop an exact partial differential equation-based methodology that predicts time-energy optimal paths for autonomous vehicles navigating in dynamic environments. The differential equations solve the multi-objective optimization problem of navigating a vehicle autonomously in a dynamic flow field to any destination with the goal of minimizing travel time and energy use. Based on Hamilton-Jacobi theory for reachability and the level set method, the methodology computes the exact Pareto optimal solutions to the multi-objective path planning problem, numerically solving the equations governing time-energy reachability fronts and optimal paths. Our approach is applicable to path planning in various scenarios, however we primarily present examples of navigating in dynamic marine environments. First, we validate the methodology through a benchmark case of crossing a steady front (a highway flow) for which we compare our results to semi-analytical optimal path solutions. We then consider more complex unsteady environments and solve for time-energy optimal missions in a quasi-geostrophic double-gyre ocean flow field.
by Manan Doshi.
S.M.
S.M. Massachusetts Institute of Technology, Center for Computational Science & Engineering

The analysis of signals stemming from a physical system is crucial for the experimental investigation of the underlying dynamics that drives the system itself. The field of time series analysis comprises a wide variety of techniques developed with the purpose of characterizing signals and, ultimately, of providing insights on the phenomena that govern the temporal evolution of the generating system. A renowned example in this field is given by spectral analysis: the use of Fourier or Laplace transforms to bring time-domain signals into the more convenient frequency space allows to disclose the key features of linear systems. A more complex scenario turns up when nonlinearity intervenes within a system's dynamics. Nonlinear coupling between a system's degrees of freedom brings about interesting dynamical regimes, such as self-sustained periodic (though anharmonic) oscillations ("limit cycles"), or quasi-periodic evolutions that exhibit sharp spectral lines while lacking strict periodicity ("limit tori"). Among the consequences of nonlinearity, the onset of chaos is definitely the most fascinating one. Chaos is a dynamical regime characterized by unpredictability and lack of periodicity, despite being generated by deterministic laws. Signals generated by chaotic dynamical systems appear as irregular: the corresponding spectra are broad and flat, prediction of future values is challenging, and evolutions within the systems' state spaces converge to strange attractor sets with noninteger dimensionality. Because of these properties, chaotic signals can be mistakenly classified as noise if linear techniques such as spectral analysis are used. The identification of chaos and its characterization require the assessment of dynamical invariants that quantify the complex features of a chaotic system's evolution. For example, Lyapunov exponents provide a marker of unpredictability; the estimation of attractor dimensions, on the other hand, highlights the unconventional geometry of a chaotic system's state space. Nonlinear time series analysis techniques act directly within the state space of the system under investigation. However, experimentally, full access to a system's state space is not always available. Often, only a scalar signal stemming from the dynamical system can be recorded, thus providing, upon sampling, a scalar sequence. Nevertheless, by virtue of a fundamental theorem by Takens, it is possible to reconstruct a proxy of the original state space evolution out of a single, scalar sequence. This reconstruction is carried out by means of the so-called embedding procedure: m-dimensional vectors are built by picking successive elements of the scalar sequence delayed by a lag L. On the other hand, besides posing some necessary conditions on the integer embedding parameters m and L, Takens' theorem does not provide any clue on how to choose them correctly. Although many optimal embedding criteria were proposed, a general answer to the problem is still lacking. As a matter of fact, conventional methods for optimal embedding are flawed by several drawbacks, the most relevant being the need for a subjective evaluation of the outcomes of applied algorithms. Tackling the issue of optimally selecting embedding parameters makes up the core topic of this thesis work. In particular, I will discuss a novel approach that was pursued by our research group and that led to the development of a new method for the identification of suitable embedding parameters. Rather than most conventional approaches, which seek a single optimal value for m and L to embed an input sequence, our approach provides a set of embedding choices that are equivalently suitable to reconstruct the dynamics. The suitability of each embedding choice m, L is assessed by relying on statistical testing, thus providing a criterion that does not require a subjective evaluation of outcomes. The starting point of our method are embedding-dependent correlation integrals, i.e. cumulative distributions of embedding vector distances, built out of an input scalar sequence. In the case of Gaussian white noise, an analytical expression for correlation integrals is available, and, by exploiting this expression, a gauge transformation of distances is introduced to provide a more convenient representation of correlation integrals. Under this new gauge, it is possible to test—in a computationally undemanding way—whether an input sequence is compatible with Gaussian white noise and, subsequently, whether the sequence is compatible with the hypothesis of an underlying chaotic system. These two statistical tests allow ruling out embedding choices that are unsuitable to reconstruct the dynamics. The estimation of correlation dimension, carried out by means of a newly devised estimator, makes up the third stage of the method: sets of embedding choices that provide uniform estimates of this dynamical invariant are deemed to be suitable to embed the sequence.The method was successfully applied to synthetic and experimental sequences, providing new insight into the longstanding issue of optimal embedding. For example, the relevance of the embedding window (m-1)L, i.e. the time span covered by each embedding vector, is naturally highlighted by our approach. In addition, our method provides some information on the adequacy of the sampling period used to record the input sequence.The method correctly distinguishes a chaotic sequence from surrogate ones generated out of it and having the same power spectrum. The technique of surrogate generation, which I also addressed during my Ph. D. work to develop new dedicated algorithms and to analyze brain signals, allows to estimate significance levels in situations where standard analytical algorithms are unapplicable. The novel embedding approach being able to tell apart an original sequence from surrogate ones shows its capability to distinguish signals beyond their spectral—or autocorrelation—similarities.One of the possible applications of the new approach concerns another longstanding issue, namely that of distinguishing noise from chaos. To this purpose, complementary information is provided by analyzing the asymptotic (long-time) behaviour of the so-called time-dependent divergence exponent. This embedding-dependent metric is commonly used to estimate—by processing its short-time linearly growing region—the maximum Lyapunov exponent out of a scalar sequence. However, insights on the kind of source generating the sequence can be extracted from the—usually overlooked—asymptotic behaviour of the divergence exponent. Moreover, in the case of chaotic sources, this analysis also provides a precise estimate of the system's correlation dimension. Besides describing the results concerning the discrimination of chaotic systems from noise sources, I will also discuss the possibility of using the related correlation dimension estimates to improve the third stage of the method introduced above for the identification of suitable embedding parameters. The discovery of chaos as a possible dynamical regime for nonlinear systems led to the search of chaotic behaviour in experimental recordings. In some fields, this search gave plenty of positive results: for example, chaotic dynamics was successfully identified and tamed in electronic circuits and laser-based optical setups. These two families of experimental chaotic systems eventually became versatile tools to study chaos and its possible applications. On the other hand, chaotic behaviour is also looked for in climate science, biology, neuroscience, and even economics. In these fields, nonlinearity is widespread: many smaller units interact nonlinearly, yielding a collective motion that can be described by means of few, nonlinearly coupled effective degrees of freedom. The corresponding recorded signals exhibit, in many cases, an irregular and complex evolution. A possible underlying chaotic evolution—as opposed to a stochastic one—would be of interest both to reveal the presence of determinism and to predict the system's future states. While some claims concerning the existence of chaos in these fields have been made, most results are debated or inconclusive. Nonstationarity, low signal-to-noise ratio, external perturbations and poor reproducibility are just few among the issues that hinder the search of chaos in natural systems. In the final part of this work, I will briefly discuss the problem of chasing chaos in experimental recordings by considering two example sequences, the first one generated by an electronic circuit and the second one corresponding to recordings of brain activity. The present thesis is organized as follows. The core concepts of time series analysis, including the key features of chaotic dynamics, are presented in Chapter 1. A brief review of the search for chaos in experimental systems is also provided; the difficulties concerning this quest in some research fields are also highlighted. Chapter 2 describes the embedding procedure and the issue of optimally choosing the related parameters. Thereupon, existing methods to carry out the embedding choice are reviewed and their limitations are pointed out. In addition, two embedding-dependent nonlinear techniques that are ordinarily used to characterize chaos, namely the estimation of correlation dimension by means of correlation integrals and the assessment of maximum Lyapunov exponent, are presented. The new approach for the identification of suitable embedding parameters, which makes up the core topic of the present thesis work, is the subject of Chapter 3 and 4. While Chapter 3 contains the theoretical outline of the approach, as well as its implementation details, Chapter 4 discusses the application of the approach to benchmark synthetic and experimental sequences, thus illustrating its perks and its limitations. The study of the asymptotic behaviour of the time-dependent divergent exponent is presented in Chapter 5. The alternative estimator of correlation dimension, which relies on this asymptotic metric, is discussed as a possible improvement to the approach described in Chapters 3, 4. The search for chaos out of experimental data is discussed in Chapter 6 by means of two examples of real-world recordings. Concluding remarks are finally drawn in Chapter 7.

Moving toward ubiquitous Cyber-Physical Systems - where computation, control and communication units are mutually interacting - this thesis aims to provide fundamental frameworks to address the problems arising from such a system, namely the real-time multiprocessor scheduling problem (RTMSP) and the multi-UAV topology control problem (MUTCP). The RTMSP is concerned with how tasks can be scheduled on available computing resources such that no task misses a deadline. An optimization-based control method was used to solve the problem. Though it is quite natural to formulate the task assignment problem as a mixed-integer nonlinear program, the computation cost is high. By reformulating the scheduling problem as a problem of first determining a percentage of task execution time and then finding the task execution order, the computation complexity can be reduced. Simulation results illustrate that our methods are both feasibility optimal and energy optimal. The framework is then extended to solve a scheduling problem with uncertainty in task execution times by adopting a feedback approach. The MUTCP is concerned with how a communication network topology can be determined such that the energy cost is minimized. An optimal control framework to construct a data aggregation network is proposed to optimally trade-off between communication and computation energy. The benefit of our network topology model is that it is a self-organized multi-hop hierarchical clustering network, which provides better performance in term of energy consumption, reliability and network scalability. In addition, our framework can be applied to both homogeneous and heterogeneous mobile sensor networks due to the generalization of the network model. Two multi-UAV information gathering applications, i.e. target tracking and area mapping, were chosen to test the proposed algorithm. Based on simulation results, our method can save up to 40% energy for a target tracking and 60% for an area mapping compared to the baseline approach.

Real-time systems are composed of a set of tasks that must respect some deadlines. We find them in applications as diversified as the telecommunications, medical devices, cars, planes, satellites, military applications, etc. Missing deadlines in a real-time system may cause various results such as a diminution of the quality of service provided by the system, the complete stop of the application or even the death of people. Being able to prove the correct operation of such systems is therefore primordial. This is the goal of the real-time scheduling theory.

These last years, we have witnessed a paradigm shift in the computing platform architectures. Uniprocessor platforms have given place to multiprocessor architectures. While the real-time scheduling theory can be considered as being mature for uniprocessor systems, it is still an evolving research field for multiprocessor architectures. One of the main difficulties with multiprocessor platforms, is to provide an optimal scheduling algorithm (i.e. scheduling algorithm that constructs a schedule respecting all the task deadlines for any task set for which a solution exists). Although optimal multiprocessor real-time scheduling algorithms exist, they usually cause an excessive number of task preemptions and migrations during the schedule. These preemptions and migrations cause overheads that must be added to the task execution times. Therefore, task sets that would have been schedulable if preemptions and migrations had no cost, become unschedulable in practice. An efficient scheduling algorithm is therefore an algorithm that either minimize the number of preemptions and migrations, or reduce their cost.

In this dissertation, we expose the following results:

- We show that reducing the "fairness" in the schedule, advantageously impacts the number of preemptions and migrations. Hence, all the scheduling algorithms that will be proposed in this thesis, tend to reduce or even suppress the fairness in the computed schedule.

- We propose three new online scheduling algorithms. One of them --- namely, BF2 --- is optimal for the scheduling of sporadic tasks in discrete-time environments, and reduces the number of task preemptions and migrations in comparison with the state-of-the-art in discrete-time systems. The second one is optimal for the scheduling of periodic tasks in a continuous-time environment. Because this second algorithm is based on a semi-partitioned scheme, it should favorably impact the preemption overheads. The third algorithm --- named U-EDF --- is optimal for the scheduling of sporadic and dynamic task sets in a continuous-time environment. It is the first real-time scheduling algorithm which is not based on the notion of "fairness" and nevertheless remains optimal for the scheduling of sporadic (and dynamic) systems. This important result was achieved by extending the uniprocessor algorithm EDF to the multiprocessor scheduling problem.

- Because the coding techniques are also evolving as the degree of parallelism increases in computing platforms, we provide solutions enabling the scheduling of parallel tasks with the currently existing scheduling algorithms, which were initially designed for the scheduling of sequential independent tasks.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished