The existing literature determining the optimal rotation period of a forest stand under conditions of certainty, as well as under uncertainty, lacks the genera 1 scope to be useful. A forest provides timber of commercial value, a flow of recreational services, and other valuable environmental s ervices. Providing goods and services invo lves benefits as well as costs. Relevant management decisions depend on the net va 1 ues that can be obtai ned. The present work developes a more general model for determining an optimal rotation period incorporating various fixed and variable costs associated with timber production and recreational services in an environment of certainty and uncertainty. It is shown that under certainty, the optimal rotation period is likely to be finite and depending on the values of benefits and costs the rotation period indicated by the solution of this model may be identical to, shorter, or longer than that indicated by a model ignoring net values. In addition, a generalized Faustmann rule under certainty (when only recreational value i s added to the model ) using optimal control (maximum principle) as the analytical tool has been developed and the impact of two sources of uncertainties on the optimal rotation decision in the context of the more generalized model is analyzed. They are (1) uncertainty related to future stumpage price, and (2) uncertainty related to the future stock of trees due to unpredictable natural catastrophes. Under price uncertainty the optimal rotation period will be longer than that under conditions of certainty if the forest operator is risk averse. In addition, the period wi ll be lengthened with increasing risk and shortened with increasing expected stumpage price under noni ncreasing absolute risk aversion of the forest operator. The risk of catastrophic destruction of the biomass whether total or partial will lead to a rotation period dependent on the value of the average rate of occurrence of catastrophes.

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.

With the fast development of communication systems, computers and consumer electronics, the power supplies for telecoms, servers, desktops, laptops, flat-panel TVs, LED lighting, etc. are required for more power delivery with smaller spaces. The LLC resonant converter has been widely adopted for these applications due to the advantages in high efficiency, high power density and holdup time operation capability. However, unlike PWM converters, the control of the LLC resonant converter is much more difficult because of the fast dynamic characteristic of the resonant tank. In some highly dynamic processes like the load transient, start-up, over-load protection and burst operation, it is hard to control the current and voltage stresses and oscillations in the resonant tank. Moreover, to meet the high power density requirement, the LLC is required to operate at a high switching frequency. Thus the driving of the synchronous rectifier (SR) poses a design challenge as well. To analyze the fast dynamic characteristic, a graphic state-plane technique has been adopted for a class of resonant converters. In this work, it has been extended to the LLC resonant converter. First of all, the LLC steady state and dynamic behaviors are analyzed in the state plane. After that, a simplified implementation of the optimal trajectory control is proposed to significantly improve the load transient response: the new steady state can be tracked in the minimal period of time. With the advantages of the state-trajectory analysis and digital control, the LLC soft start-up is optimized as well. The current and voltage stress is limited in the resonant tank during the start-up process. The output voltage is built up quickly and smoothly. Furthermore, the LLC burst mode is investigated and optimized in the state plane. Several optimal switching patterns are proposed to improve the light load efficiency and minimize the dynamic oscillations. During the burst on-time, the LLC can be controlled to track the steady state of the best efficiency load condition in one-pulse time. Thus, high light-load efficiency is accomplished. Finally, an intelligent SR driving scheme is proposed and its simple digital implementation is introduced. By sensing the SR drain to source voltage and detecting the paralleled body diode conduction, the SR gate driving signal can be tuned within all operating frequency regions. In conclusion, this work not only solves some major academic problems about analysis and control of the LLC resonant converter based on the graphic state plane, but also makes significant contributions to the industry by improving the LLC transient responses and overall efficiency. / Ph. D.

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Revenue insurance with shallow loss protection for farmers has been introduced recently. A common attribute of most shallow loss proposals is that they would be arearevenue triggered. The impact on optimal hedge ratios of combining these shallow loss insurance proposals with deep loss farm-level insurance is examined. Since crop insurance, commodity programs and forward pricing are commonly used concurrently to manage crop revenue risk, the optimal combinations of these tools are explored. Numerical analysis in the presence of yield, basis and futures price variability is used to find the futures hedge ratio which maximizes the certainty equivalent of a risk averse producer. The results generally reveal a lower optimal hedge ratio with area-insurance than with individual insurance and show that shallow loss revenue insurance tends to slightly increase optimal hedge ratios.

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Optimal control design and implementation for nonlinear systems is a topic of much interest. However, unlike for linear systems, for nonlinear systems explicit analytical solution for optimal feedback control is not available. Numerical techniques, on the other hand, can be used to approximate the solution of the HJB equation to find the optimal control. In this research, a computational approach is developed for finding the optimal control for nonlinear systems with polynomial vector fields based on sum of squares technique. In this research, a numerical technique is developed for optimal control of polynomial nonlinear systems. The approach follows a four-step procedure to obtain both local and approximate global optimality. In the first step, local optimal control is found by using the linearization method and solving the Algebraic Riccati equation with respect to the quadratic part of a given performance index. Next, we utilize the density function method to find a globally stabilizing polynomial nonlinear control for the nonlinear system. In the third step, we find a corresponding Lyapunov function for the designed control in the previous steps based on the Hamilton Jacobi inequality by using semidefinite programming. Finally, to achieve global optimality, we iteratively update the pair of nonlinear control and Lyapunov function based on a state-dependent polynomial matrix inequality. Numerical examples illustrate the effectiveness of the design approach.

The duty cycle control (DCC) modulation scheme for the three-phase dual-active-bridge (3p-DAB) DC-DC converter is a promising three degree-of-freedom modulation scheme which can extend the converter’s soft-switching range and reduce conduction losses under partial loading and wide voltage variations. However, the prior suggested methods to implement DCC in 3p-DABs have drawbacks such as requiring a multi-frequency approximation and offline optimization process or achieving less than optimal efficiency. To overcome these challenges, this research first proposes an optimal DCC modulation strategy (OMS) for the 3p-DAB based on a novel piece-wise time-domain analysis (TDA) and optimization process that obtains the optimal control parameters for minimum RMS phase current. Secondly, this research proposes a novel closed-form minimum current stress optimization (MCSO) DCC scheme based on the theoretical findings of the TDA optimization. The MCSO reduces the transformer phase currents and extends soft-switching operation under partial loading and wide voltage variations. Experimental results via open-loop testing show that the proposed closed-form MCSO DCC scheme has virtually identical efficiency as the OMS, making this the first research to provide a closed-form DCC modulation scheme for a 3p-DAB that achieves efficiency results equivalent to a fully-optimized offline scheme, but without the drawbacks of the offline optimization process. / Thesis / Master of Applied Science (MASc)

There has been growing interest in the role of motivation in motor learning, and specifically how autonomy, competence, and intrinsic motivation may directly benefit the skill acquisition process. Within the autonomy branch of the motivation pillar in OPTIMAL theory, supporting a learner’s basic psychological need for autonomy contributes to a virtuous cycle that enhances expectancies for success (i.e., perceptions of competence) and in turn facilitates motor performance and learning. Although many experiments have concluded support for OPTIMAL theory, these studies have often relied on small sample sizes, have not been pre-registered, and have consistently failed to include appropriate measures that assess key predictions in the theory. The purpose of this dissertation was to address these methodological limitations and test core predictions in the OPTIMAL theory regarding the direct and causal role of autonomy-supportive practice conditions—control over practice and instructional language—on motor performance and learning. Experiments 1 and 2 (Chapter 2) critically tested between the information-processing and motivation-based (i.e., OPTIMAL theory) explanations of the self-controlled learning advantage by providing participants in choice and yoked groups with error or graded feedback (Experiment 1) and binary feedback (Experiment 2). Results showed no self-controlled learning advantage and exercising choice in practice did not increase perceptions of autonomy, competence, or intrinsic motivation, nor did it improve error estimation accuracy. Although these findings are difficult to reconcile with either explanation, they are consistent with a growing body of evidence suggesting self-controlled conditions are not advantageous for motor learning. Experiment 3 addressed a methodological limitation of past self-controlled learning research by including a novel yoked group that was explicitly told they were being denied choice and that their observation schedule was created by another participant. Results showed no self-controlled learning advantage despite finding higher perceptions of autonomy in the choice group. These findings are consistent with Experiments 1 and 2, and further questions the causal role of autonomy-support on motor learning and the robustness of the so-called self-controlled learning advantage. Experiment 4 investigated the influence of different instructional language styles on skill acquisition. Throughout practice participants received task instructions that used either autonomy-supportive or controlling language. Results showed no performance differences in acquisition or retention despite finding higher perceptions of autonomy and competence in the autonomy-supportive group. These findings are inconsistent with key predictions in OPTIMAL theory regarding the role of autonomy in motor learning. / Dissertation / Doctor of Philosophy (PhD) / Practice environments that provide learners with autonomy have been argued to be more effective for learning new motor skills compared to more controlling environments. Two techniques that can be used to create autonomy-supportive learning environments are giving learners control over a feature of their practice or the language used when giving task instructions. This dissertation addresses knowledge gaps and several methodological limitations of previous literature by measuring key psychological variables, the use of novel experimental groups, large N studies, modern statistical techniques, and open science practices. Findings showed that under many conditions perceptions of autonomy and competence can be impacted positively; however, these psychological benefits do not reliably translate into superior motor performance or learning. Collectively, results of this dissertation challenge mainstream perspectives regarding a direct and causal role of motivational influences on motor skill acquisition.

This dissertation presents a new algorithm for optimal power flow in distribution systems. The new algorithm, Discrete Ascent Optimal Programming (DAOP), will converge to the same solution as the Lagrange multiplier approach as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. Because no partial derivatives, solutions of simultaneous equations, or matrix operations are required, the DAOP algorithm is simple to apply and program. DAOP is especially suited for programming with pointers. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required to reach a solution. In addition to optimal power flow, the algorithm, heuristic in nature, can be applied to switch placement design, reconfiguration, and economic dispatch. The basic principles of the algorithm have been used to devise a phase balancing routine which has been implemented in the Distribution Engineering Workstation (DEWorkstation) software package sponsored by the Electric Power Research Institute (EPRI). The new algorithm presented in this dissertation works toward a solution by performing a series of calculations within a finite number of steps. At the start of the algorithm, the assumption is made that no power is flowing in the system. Each step adds a discrete unit of load to the system in such a fashion as to minimize loss. As progress toward the solution is made, more and more load is satisfied and the losses in the system continue to increase. The algorithm is terminated when all system load is satisfied. When the algorithm is finished, the sources which should supply each load have been identified along with the amount of power delivered by each source. Discussion will show that the method will converge to a solution that is within the discrete step size of the optimum. The algorithm can be thought of as an ascent method because the cost (losses) continually increases as more and more load is satisfied. Hence, the name Discrete Ascent Optimal Programming (DAOP) has been given to the algorithm. The new algorithm uses the topology of the power system such that the entire system is not considered at each step. Therefore, DAOP is not an exhaustive state enumeration scheme. Only those portions of the system containing loads most closely connected (via least loss paths) to the sources are first considered. As loads become supplied during the course of the solution, other loads are considered and supplied until the system is fully loaded. / Ph. D.