Dissertations / Theses on the topic 'Quadratic cost'

We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice to calculate optimal inventory level, would be very costly. Our algorithm uses quadratic splines to approximate the optimal cost function for this dynamic inventory problem and calculates the optimal inventory level and optimal cost.

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Economics from the NOVA – School of Business and Economics
In a context of intensive structural reform, this paper estimates optimum bed-sizes for the Portuguese public hospitals. Considering costs and production data for the period 2003-2006, we estimate a production-theoretic quadratic cost-function, adjusted to better describe the underlying technology. Room for short-run scale-economies exploitation is found, but long-run scale-diseconomies are unambiguous. In light of these predictions and of an optimum around 233 fully-occupied beds, there is mixed evidence of potential gains from two hospital mergers and from one of the forthcoming constructions of public hospitals. The results are expected to contribute to shape the hospital network in a cost-efficient manner.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O presente trabalho apresenta o método primal-dual previsor-corretor de pontos interiores para programação quadrática, com restrições lineares e quadráticos e variáveis canalizadas, e a aplicação deste método na resolução de problemas multiobjetivo de despacho econômico e ambiental, encontrados na engenharia elétrica. Pretende-se determinar soluções que sejam eficientes em relação ao custo dos combustíveis empregados na geração termoelétrica de energia e ao controle da emissão de poluentes, investigando-se duas estratégias: a primeira estratégica considera na função objetivo a soma ponderada entre as funções objetivo econômica e objetivo ambiental; a segunda estratégia considera o problema de despacho econômico condicionado à restrição ambiental, limitada superiormente para níveis permissíveis de missão. Para a resolução destes, uma implementação computacional do método primal-dual foi realizada em linguagem de programação C++, considerando o procedimento previsor-corretor com uma estratégia de barreira modificada para as restrições quadráticas de desigualdade, quando consideramos a segunda estratégia. Os resultados obtidos demonstram a eficiência do método em destaque em comparação a outros métodos como algoritmos genéticos co-evolutivo, atávico híbrido e cultural, bem como ao método primal-dual de pontos interiores, com procedimento de busca unidimensional, que estão divulgados na literatura
This paper presents the primal-dual predictor-corrector interior point method for quadratic programming with linear and quadratic constraints and bounded variables, and its application in multiobjective problems of economic and environmental dispatch, found in electrical engineering. It is intended to determine effective solutions to the fuel cost used in thermal power generation and emissions control, by investigating two strategy; the first strategy considers the objective function as weighted sum of economic and environmental objective functions; the second strategy considers the economic dispatch problem subject to environmental constraint, upper bounded for allowable emission levels. To solve them, a computational implementation of primal-dual methods was performed in C++ programming language, considering the predictor-corrector procedure with a strategy of modified barrier for the quadratic inequality constraints, when we considerer the second strategy. The results obtained demonstrate the efficiency of the method highlighted in comparison with the co-evolutive genetic algorithms, hybrid and atavistic cultural, as well the primal-dual interior point method with one-dimensional search procedure, which are found in the literature

Orientador: Antonio Roberto Balbo
Banca: Helenice de Oliveira F. Silva
Banca: Edmea Cassia Baptista
Resumo: O presente trabalho apresenta o método primal-dual previsor-corretor de pontos interiores para programação quadrática, com restrições lineares e quadráticos e variáveis canalizadas, e a aplicação deste método na resolução de problemas multiobjetivo de despacho econômico e ambiental, encontrados na engenharia elétrica. Pretende-se determinar soluções que sejam eficientes em relação ao custo dos combustíveis empregados na geração termoelétrica de energia e ao controle da emissão de poluentes, investigando-se duas estratégias: a primeira estratégica considera na função objetivo a soma ponderada entre as funções objetivo econômica e objetivo ambiental; a segunda estratégia considera o problema de despacho econômico condicionado à restrição ambiental, limitada superiormente para níveis permissíveis de missão. Para a resolução destes, uma implementação computacional do método primal-dual foi realizada em linguagem de programação C++, considerando o procedimento previsor-corretor com uma estratégia de barreira modificada para as restrições quadráticas de desigualdade, quando consideramos a segunda estratégia. Os resultados obtidos demonstram a eficiência do método em destaque em comparação a outros métodos como algoritmos genéticos co-evolutivo, atávico híbrido e cultural, bem como ao método primal-dual de pontos interiores, com procedimento de busca unidimensional, que estão divulgados na literatura
Abstract: This paper presents the primal-dual predictor-corrector interior point method for quadratic programming with linear and quadratic constraints and bounded variables, and its application in multiobjective problems of economic and environmental dispatch, found in electrical engineering. It is intended to determine effective solutions to the fuel cost used in thermal power generation and emissions control, by investigating two strategy; the first strategy considers the objective function as weighted sum of economic and environmental objective functions; the second strategy considers the economic dispatch problem subject to environmental constraint, upper bounded for allowable emission levels. To solve them, a computational implementation of primal-dual methods was performed in C++ programming language, considering the predictor-corrector procedure with a strategy of modified barrier for the quadratic inequality constraints, when we considerer the second strategy. The results obtained demonstrate the efficiency of the method highlighted in comparison with the co-evolutive genetic algorithms, hybrid and atavistic cultural, as well the primal-dual interior point method with one-dimensional search procedure, which are found in the literature
Mestre

Networked embedded control systems are present almost everywhere. A recent trendis to introduce radio communication in these systems to increase mobility and flex-ibility. Network nodes, such as the sensors, are often simple devices with limitedcomputing and transmission power and low storage capacity, so an important prob-lem concerns how to optimize the use of resources to provide sustained overall sys-tem performance. The approach to this problem taken in the thesis is to analyzeand design the communication and control application layers in an integrated man-ner. We focus in particular on cross-layer design techniques for closed-loop controlover non-ideal communication channels, motivated by future control systems withvery low-rate and highly quantized sensor communication over noisy links. Severalfundamental problems in the design of source–channel coding and optimal controlfor these systems are discussed.The thesis consists of three parts. The first and main part is devoted to the jointdesign of the coding and control for linear plants, whose state feedback is trans-mitted over a finite-rate noisy channel. The system performance is measured by afinite-horizon linear quadratic cost. We discuss equivalence and separation proper-ties of the system, and conclude that although certainty equivalence does not holdin general it can still be utilized, under certain conditions, to simplify the overalldesign by separating the estimation and the control problems. An iterative opti-mization algorithm for training the encoder–controller pairs, taking channel errorsinto account in the quantizer design, is proposed. Monte Carlo simulations demon-strate promising improvements in performance compared to traditional approaches.In the second part of the thesis, we study the rate allocation problem for statefeedback control of a linear plant over a noisy channel. Optimizing a time-varyingcommunication rate, subject to a maximum average-rate constraint, can be viewedas a method to overcome the limited bandwidth and energy resources and to achievebetter overall performance. The basic idea is to allow the sensor and the controllerto communicate with a higher data rate when it is required. One general obstacle ofoptimal rate allocation is that it often leads to a non-convex and non-linear problem.We deal with this challenge by using high-rate theory and Lagrange duality. It isshown that the proposed method gives a good performance compared to some otherrate allocation schemes.In the third part, encoder–controller design for Gaussian channels is addressed.Optimizing for the Gaussian channel increases the controller complexity substan-tially because the channel output alphabet is now infinite. We show that an efficientcontroller can be implemented using Hadamard techniques. Thereafter, we proposea practical controller that makes use of both soft and hard channel outputs.
QC 20100623

This doctoral thesis consists of three essays. In the first essay I investigate the presence of productivity convergence in eight regional pulp and paper industries of U.S. and Canada over the period of 1971-2005. Expectation of productivity convergence in the pulp and paper industries of Canadian provinces and of the states of its southern neighbour is high since they are trading partners with fairly high level of exchanges in both pulp and paper products. Moreover, they share a common production technology that changed very little over the last century. I supplement the North-American regional data with national data for two Nordic countries, Finland and Sweden, which provides a scope to compare the productivity performances of four leading players in global pulp and paper industry. I find evidence in favour of the catch-up hypothesis among the regional pulp and paper industries of U.S. and Canada in my sample. The growth performance is at the advantage of Canadian provinces relative to their U.S. counterparts. However, it is not good enough to surpass the growth rates of this industry in the two Nordic countries. It is well-known that econometric productivity estimation using flexible functional forms often encounter violations of curvature conditions. However, the productivity literature does not provide any guidance on the selection of appropriate functional forms once they satisfy the theoretical regularity conditions. The second chapter of my thesis provides an empirical evidence that imposing local curvature conditions on the flexible functional forms affect total factor productivity (TFP) estimates in addition to the elasticity estimates. Moreover, I use this as a criterion for evaluating the performances of three widely used locally flexible cost functional forms - the translog (TL), the Generalized Leontief (GL), and the Normalized Quadratic (NQ) - in providing TFP estimates. Results suggest that the NQ model performs better than the other two functional forms in providing TFP estimates. The third essay capitalizes on newly available high frequency energy consumption data from commercial buildings in the District of Columbia (DC) to provide novel insights on the realized energy use impacts of energy efficiency standards in commercial buildings. Combining these data with hourly weather data and information on tenancy contract structure I evaluate the impacts of energy standards, contractual structure of utility bill payments, and energy star labeling on account level electricity consumption. Using this unique panel dataset, the analysis takes advantage of detailed building-level characteristics and the heterogeneity in the building age distribution, resulting in buildings constructed before and after mandatory energy standards came into effect. Estimation results suggest that in commercial buildings constructed under a code, electricity consumption is lower by about 0.48 kWh per cooling degree hour. When tenants pay for their own utilities, consumption is lower by 0.82 kWh per cooling degree hour. The Energy Star effect is a 0.31 kWh reduction per cooling degree hour. Finally, peak savings for all three variables of interest occur at 2pm in the summer months, whereas peak summer marginal prices at DC's local electric utility occur at 5pm.

This thesis describes the theory of model predictive control and application of the theory to synchronous drives. It shows explicit and on-line solutions and compares the results with classical vector control structure.

On aborde la commande predictive avec contraintes, basee sur la minimisation d'un critere quadratique a horizon fini fuyant, et la commande predictive sous contraintes avec placement de poles asymptotiques. Test du comportement de la commande predictive avec une enceinte climatique multivariable

Stink bugs are beginning to emerge as important pests of cotton that often require management in the Lower Texas Gulf Coast. As eradication of the boll weevil progresses and producers increasingly adopt transgenic cotton varieties resulting in reduced broad spectrum pesticide use, stink bugs will likely become key cotton pests in this area. The Lower Texas Gulf Coast has a stink bug complex that differs somewhat from other areas of the Cotton Belt. Euschistus servus and lesser brown stink bugs, including E. quadrator, E. obscurus, E. crassus, and E. ictericus, make up the largest portion of this pest complex, and green/southern green stink bugs play less important roles than in other areas. Using evidence of internal feeding as a sampling criterion detected stink bug infestations more frequently that when using visual or drop cloth sampling methods. The main drawback to using this method is that species composition may still need to be determined when an economic threshold is reached in order to select the most effective control. Euschistus servus and E. quadrator both caused significant reductions in yield and fiber quality in cotton bolls, but E. servus was able to reduce yield and quality in small (1.8 cm), medium (2.8 cm), and large (3.2 cm) bolls, whereas E. quadrator reduced yield in only small bolls and reduced quality in only small and medium bolls. In general, E. servus caused more damage to bolls than E. quadrator and was able to damage a wider range of boll sizes. Dicrotophos was the most effective insecticide for stink bug control. Exposure to pyrethroids caused high mortality in N. viridula similar to that of dicrotophos, but pyrethroid activity was more variable when E. servus were exposed. In general, E. quadrator was more susceptible to insecticide treatments than E. servus, but both had similar mortalities when exposed to organophosphates, pyrethroids, and carbamates. Dynamic evidence of internal feeding thresholds may potentially be the best method for determining the need for stink bug control in cotton, but further research is necessary to refine these thresholds and make them applicable to the Lower Texas Gulf Coast.

Pour un problème de commande optimale linéaire-quadratique monocritère les lois de commande partiellement en boucle fermée à deux niveaux sont étudiées. Une généralisation des moyens de synthèse de ces lois est proposée. Pour les problèmes multicritères linéaires-quadratiques, l'utilisation des stratégies de Nash et de Stackelberg nécessite la résolution d'un ensemble d'équations matricielles couplées. La solution analytique exacte de tous les jeux de Stackelberg en boucle ouverte et d'une large classe des jeux de Nash est obtenue. Ces résultats s'appuient sur les propriétés des spectres des matrices caractérisant les conditions nécessaires à satisfaire par les différentes stratégies.

La conception de l'appareillage électrique relève dune méthodologie généralement fort complexe. Les problèmes posés par la conception de l'appareillage électrique sont analysés et montrent l'inefficacité des méthodes mathématiques. Une approche ensembliste floue est exposée et permet de modéliser l'aspect heuristique du problème ainsi que les aspects scientifiques et industriels de la conception. Un système expert d'aide à la conception des disjoncteurs à arc tournant a été réalisé. Les résultats obtenus sont commentés et montrent l'intérêt d'une telle approche

Beaucoup de résultats sur l’estimation d’une matrice d’échelle en analyse multidimensionnelle sont obtenus sous l’hypothèse de normalité (condition sous laquelle il s’agit de la matrice de covariance). Or il s’avère que, dans des domaines tels que la gestion de portefeuille en finance, cette hypothèse n’est pas très appropriée. Dans ce cas, la famille des distributions à symétrie elliptique, qui contient la distribution gaussienne, est une alternative intéressante. Nous considérons dans cette thèse le problème d’estimation de la matrice d’échelle Σ du modèle additif Yp_m = M + E, d’un point de vue de la théorie de la décision. Ici, p représente le nombre de variables, m le nombre d’observations, M une matrice de paramètres inconnus de rang q < p et E un bruit aléatoire de distribution à symétrie elliptique, avec une matrice de covariance proportionnelle à Im x Σ. Ce problème d’estimation est abordé sous la représentation canonique de ce modèle où la matrice d’observation Y est décomposée en deux matrices, à savoir, Zq x p qui résume l’information contenue dans M et une matrice Un x p, où n = m - q, qui résume l’information suffisante pour l’estimation de Σ. Comme les estimateurs naturels de la forme Σa = a S (où S = UT U et a est une constante positive) ne sont pas de bons estimateurs lorsque le nombre de variables p et le rapport p=n sont grands, nous proposons des estimateurs alternatifs de la forme ^Σa;G = a(S + S S+G(Z; S)) où S+ est l’inverse de Moore-Penrose de S (qui coïncide avec l’inverse S-1 lorsque S est inversible). Nous fournissons des conditions sur la matrice de correction SS+G(Z; S) telles que ^Σa;G améliore^Σa sous le coût quadratique L(Σ; ^Σ) = tr(^ΣΣ‾1 - Ip)² et sous une modification de ce dernier, à savoir le coût basé sur les données LS (Σ; ^Σ) = tr(S+Σ(^ΣΣ‾1 - Ip)²). Nous adoptons une approche unifiée des deux cas où S est inversible et S est non inversible. À cette fin, une nouvelle identité de type Stein-Haff et un nouveau calcul sur la décomposition en valeurs propres de S sont développés. Notre théorie est illustrée par une grande classe d’estimateurs orthogonalement invariants et par un ensemble de simulations
Numerous results on the estimation of a scale matrix in multivariate analysis are obtained under Gaussian assumption (condition under which it is the covariance matrix). However in such areas as Portfolio management in finance, this assumption is not well adapted. Thus, the family of elliptical symmetric distribution, which contains the Gaussian distribution, is an interesting alternative. In this thesis, we consider the problem of estimating the scale matrix _ of the additif model Yp_m = M + E, under theoretical decision point of view. Here, p is the number of variables, m is the number of observations, M is a matrix of unknown parameters with rank q < p and E is a random noise, whose distribution is elliptically symmetric with covariance matrix proportional to Im x Σ. It is more convenient to deal with the canonical forme of this model where Y is decomposed in two matrices, namely, Zq_p which summarizes the information contained in M, and Un_p, where n = m - q which summarizes the information sufficient to estimate Σ. As the natural estimators of the form ^Σ a = a S (where S = UT U and a is a positive constant) perform poorly when the dimension of variables p and the ratio p=n are large, we propose estimators of the form ^Σa;G = a(S + S S+G(Z; S)) where S+ is the Moore-Penrose inverse of S (which coincides with S-1 when S is invertible). We provide conditions on the correction matrix SS+G(Z; S) such that ^Σa;G improves over ^Σa under the quadratic loss L(Σ; ^Σ) = tr(^ΣΣ‾1 - Ip)² and under the data based loss LS (Σ; ^Σ) = tr(S+Σ(^ΣΣ‾1 - Ip)²).. We adopt a unified approach of the two cases where S is invertible and S is non-invertible. To this end, a new Stein-Haff type identity and calculus on eigenstructure for S are developed. Our theory is illustrated with the large class of orthogonally invariant estimators and with simulations

Training a Support Vector Machine (SVM) requires the solution of a very large quadratic programming (QP) optimization problem. Sequential Minimal Optimization (SMO) is a decomposition-based algorithm which breaks this large QP problem into a series of smallest possible QP problems. However, it still costs O(n2) computation time. In our SVM implementation, we can do training with huge data sets in a distributed manner (by breaking the dataset into chunks, then using Message Passing Interface (MPI) to distribute each chunk to a different machine and processing SVM training within each chunk). In addition, we moved the kernel calculation part in SVM classification to a graphics processing unit (GPU) which has zero scheduling overhead to create concurrent threads. In this thesis, we will take advantage of this GPU architecture to improve the classification performance of SVM.

碩士
南華大學
資訊管理學研究所
95
Radio frequency identification (RFID) technology is applied extensively on daily life, such as tracking library books, supply chain, and luggage tracking within an airport. 　　 　　 Recently, Chien & Chen proposed “Mutual authentication protocol for RFID conforming to EPC”. The protocol enables to arrive mutual authentication, but the server must to compute and compare each tag in the database. Gao et al. proposed “An approach to security and privacy of RFID system for supply chain” and Gene proposed “YA-TRAP: Yet Another Trivial RFID Authentication Protocol”, these authentication schemes for RFID unable arrive mutual authentication. 　　 　　 The quadratic residue theorem is an efficacious encryption theorem, therein can get right values of the limitation of the encryption algorithm’s export control. So we further extend an authentication scheme to arrive mutual ability and apply quadratic residues theorem to reduce frequencies of searching the register table. Both the server and the tag are share it random numbers and these numbers are changed after each session that to arrive mutual authentication. That is, our method is more efficient and able to arrive mutual authentication for RFID.

碩士
國立臺北科技大學
電機工程系碩士班
91
The objective of the thesis is to find the robust T-S fuzzy controller to achieve the robust stability with optimal quadratic performance for uncertain time-delay systems. Using the T-S fuzzy model and controller, this thesis deals with the mentioned problem. With the selected Lyapunov functional, stability conditions are derived to guarantee the quadratically asymptotic stability by using Schwarz inequality and these conditions can be converted into linear matrix inequalities. Moreover, to solve the optimal quadratic cost problem, this thesis adopt the LMI technique to obtain the controller design algorithm. As a result, the optimal control for uncertain time-delay systems can be found if a common symmetric positive definite matrix P exists. The designed robust fuzzy controller provides the stability and minimizes the upper bound of cost function. From the simulation result, it is demonstrated that the derived theorems are correct and the proposed controller is feasible.

This thesis deals with a new so-called sequential quadratic Hamiltonian (SQH) iterative scheme to solve optimal control problems with differential models and cost functionals ranging from smooth to discontinuous and non-convex. This scheme is based on the Pontryagin maximum principle (PMP) that provides necessary optimality conditions for an optimal solution. In this framework, a Hamiltonian function is defined that attains its minimum pointwise at the optimal solution of the corresponding optimal control problem. In the SQH scheme, this Hamiltonian function is augmented by a quadratic penalty term consisting of the current control function and the control function from the previous iteration. The heart of the SQH scheme is to minimize this augmented Hamiltonian function pointwise in order to determine a control update. Since the PMP does not require any differ- entiability with respect to the control argument, the SQH scheme can be used to solve optimal control problems with both smooth and non-convex or even discontinuous cost functionals. The main achievement of the thesis is the formulation of a robust and efficient SQH scheme and a framework in which the convergence analysis of the SQH scheme can be carried out. In this framework, convergence of the scheme means that the calculated solution fulfills the PMP condition. The governing differential models of the considered optimal control problems are ordinary differential equations (ODEs) and partial differential equations (PDEs). In the PDE case, elliptic and parabolic equations as well as the Fokker-Planck (FP) equation are considered. For both the ODE and the PDE cases, assumptions are formulated for which it can be proved that a solution to an optimal control problem has to fulfill the PMP. The obtained results are essential for the discussion of the convergence analysis of the SQH scheme. This analysis has two parts. The first one is the well-posedness of the scheme which means that all steps of the scheme can be carried out and provide a result in finite time. The second part part is the PMP consistency of the solution. This means that the solution of the SQH scheme fulfills the PMP conditions. In the ODE case, the following results are obtained that state well-posedness of the SQH scheme and the PMP consistency of the corresponding solution. Lemma 7 states the existence of a pointwise minimum of the augmented Hamiltonian. Lemma 11 proves the existence of a weight of the quadratic penalty term such that the minimization of the corresponding augmented Hamiltonian results in a control updated that reduces the value of the cost functional. Lemma 12 states that the SQH scheme stops if an iterate is PMP optimal. Theorem 13 proves the cost functional reducing properties of the SQH control updates. The main result is given in Theorem 14, which states the pointwise convergence of the SQH scheme towards a PMP consistent solution. In this ODE framework, the SQH method is applied to two optimal control problems. The first one is an optimal quantum control problem where it is shown that the SQH method converges much faster to an optimal solution than a globalized Newton method. The second optimal control problem is an optimal tumor treatment problem with a system of coupled highly non-linear state equations that describe the tumor growth. It is shown that the framework in which the convergence of the SQH scheme is proved is applicable for this highly non-linear case. Next, the case of PDE control problems is considered. First a general framework is discussed in which a solution to the corresponding optimal control problem fulfills the PMP conditions. In this case, many theoretical estimates are presented in Theorem 59 and Theorem 64 to prove in particular the essential boundedness of the state and adjoint variables. The steps for the convergence analysis of the SQH scheme are analogous to that of the ODE case and result in Theorem 27 that states the PMP consistency of the solution obtained with the SQH scheme. This framework is applied to different elliptic and parabolic optimal control problems, including linear and bilinear control mechanisms, as well as non-linear state equations. Moreover, the SQH method is discussed for solving a state-constrained optimal control problem in an augmented formulation. In this case, it is shown in Theorem 30 that for increasing the weight of the augmentation term, which penalizes the violation of the state constraint, the measure of this state constraint violation by the corresponding solution converges to zero. Furthermore, an optimal control problem with a non-smooth L\(^1\)-tracking term and a non-smooth state equation is investigated. For this purpose, an adjoint equation is defined and the SQH method is used to solve the corresponding optimal control problem. The final part of this thesis is devoted to a class of FP models related to specific stochastic processes. The discussion starts with a focus on random walks where also jumps are included. This framework allows a derivation of a discrete FP model corresponding to a continuous FP model with jumps and boundary conditions ranging from absorbing to totally reflecting. This discussion allows the consideration of the drift-control resulting from an anisotropic probability of the steps of the random walk. Thereafter, in the PMP framework, two drift-diffusion processes and the corresponding FP models with two different control strategies for an optimal control problem with an expectation functional are considered. In the first strategy, the controls depend on time and in the second one, the controls depend on space and time. In both cases a solution to the corresponding optimal control problem is characterized with the PMP conditions, stated in Theorem 48 and Theorem 49. The well-posedness of the SQH scheme is shown in both cases and further conditions are discussed that ensure the convergence of the SQH scheme to a PMP consistent solution. The case of a space and time dependent control strategy results in a special structure of the corresponding PMP conditions that is exploited in another solution method, the so-called direct Hamiltonian (DH) method
Diese Dissertation handelt von einem neuen so genannten sequentiellen quadratischen Hamilton (SQH) iterativen Schema um Optimalsteuerungsprobleme mit Differentialmodellen und Kostenfunktionalen, die von glatt bis zu unstetig und nicht-konvex reichen, zu lösen. Dieses Schema basiert auf dem Pontryagin Maximumprinzip (PMP), welches notwendige Optimalitätsbedingungen für eine optimale Lösung zur Verfügung stellt. In diesem Rahmen wird eine Hamiltonfunktion definiert, die ihr Minimum punktweise an der optimalen Lösung des entsprechenden Optimalsteuerungsproblems annimmt. In diesem SQH Schema wird diese Hamiltonfunktion durch einen quadratischen Strafterm erweitert, der aus der aktuellen Steuerungsfunktion und der Steuerungsfunktion aus der vorherigen Iteration besteht. Das Herzstück des SQH Schemas ist die punktweise Minimierung dieser erweiterten Hamiltonfunktion um eine Aktualisierung der Steuerungsfunktion zu bestimmen. Da das PMP keine Differenzierbarkeit in Bezug auf das Steuerungsfunktionsargument verlangt, kann das SQH Schema dazu benutzt werden, Optimalsteuerungsprobleme mit sowohl glatten als auch nicht-konvexen oder sogar unstetigen Kostenfunktionalen zu lösen. Das Hauptergebnis dieser Dissertation ist die Formulierung eines robusten und effizienten SQH Schemas und eines Rahmens, in dem die Konvergenzanalyse des SQH Schemas ausgeführt werden kann. In diesem Rahmen bedeutet Konvergenz des Schemas, dass die berechnete Lösung die PMP Bedingung erfüllt. Die steuernden Differentialmodelle der betrachteten Optimalsteuerungsprobleme sind gewöhnliche Differentialgleichungen (ODEs) und partielle Differentialgleichungen (PDEs). Im PDE Fall werden elliptische und parabolische Gleichungen, sowie die Fokker-Planck (FP) Gleichung betrachtet. Für sowohl den ODE als auch den PDE Fall werden Annahmen formuliert, für die bewiesen werden kann, dass eine Lösung eines Optimalsteuerungsproblems das PMP erfüllen muss. Die erhaltenen Resultate sind für die Diskussion der Konvergenzanalyse des SQH Schemas essentiell. Diese Analyse hat zwei Teile. Der erste ist die Wohlgestelltheit des Schemas, was bedeutet, dass alle Schritte des Schemas ausgeführt werden können und ein Ergebnis in endlicher Zeit liefern. Der zweite Teil ist die PMP Konsistenz der Lösung. Das bedeutet, dass die Lösung des SQH Schemas die PMP Bedingungen erfüllt. Im ODE Fall werden die folgenden Resultate erhalten, die die Wohlgestelltheit des Schemas und die PMP Konsistenz der entsprechenden Lösung darlegen. Lemma 7 legt die Existenz eines punktweisen Minimums der erweiterten Hamiltonfunktion dar. Lemma 11 beweist die Existenz eines Gewichtes des quadratischen Strafterms, sodass die Minimierung der entsprechenden erweiterten Hamiltonfunktion zu einer Kontrollaktualisierung führt, die den Wert des Kostenfunktionals verringert. Lemma 12 legt dar, dass das SQH Schema stehen bleibt falls eine Iterierte PMP optimal ist. Satz 13 beweist die Kostenfunktional verringernden Eigenschaften der SQH Steuerungsfunktionsaktualisierung. Das Hauptresultat ist in Satz 14 gegeben, welches die punktweise Konvergenz des SQH Schemas gegen eine PMP konsistente Lösung darlegt. Das SQH-Verfahren wird in diesem ODE Rahmen auf zwei Optimalsteuerungsprobleme angewendet. Das erste ist ein optimales Quantensteuerungsproblem, bei dem gezeigt wird, dass das SQH-Verfahren viel schneller zu einer optimalen Lösung konvergiert als ein globalisiertes Newton-Verfahren. Das zweite Optimalsteuerungsproblem ist ein optimales Tumorbehandlungsproblem mit einem System gekoppelter hochgradig nicht-linearer Zustandsgleichungen, die das Tumorwachstum beschreiben. Es wird gezeigt, dass der Rahmen, in dem die Konvergenz des SQH Schemas bewiesen wird, auf diesen hochgradig nicht-linearen Fall anwendbar ist. Als nächstes wird der Fall von PDE Optimalsteuerungsprobleme betrachtet. Zunächst wird ein allgemeiner Rahmen diskutiert, in dem eine Lösung des entsprechenden Optimalsteuerungsproblem die PMP Bedingungen erfüllt. In diesem Fall werden viele theoretische Abschätzungen in Satz 59 und Satz 64 bewiesen, die insbesondere die essentielle Beschränktheit von Zustands- und Adjungiertenvariablen beweisen. Die Schritte für die Konvergenzanalyse des SQH Schemas sind analog zu denen des ODE Falls und führen zu Satz 27, der die PMP Konsistenz der Lösung, erhalten durch das SQH Schemas, darlegt. Dieser Rahmen wird auf verschiedene elliptische und parabolische Optimalsteuerungsprobleme angewendet, die lineare und bilineare Steuerungsmechanismen beinhalten, genauso wie nicht-lineare Zustandsgleichungen. Darüber hinaus wird das SQH-Verfahren zum Lösen eines zustandsbeschränkten Optimalsteuerungsproblems in einer erweiterten Formulieren diskutiert. Es wird in Satz 30 gezeigt, dass wenn man das Gewicht des Erweiterungsterms, der die Verletzung der Zustandsbeschränkung bestraft, erhöht, das Maß dieser Zustandsbeschränkungsverletzung durch die entsprechende Lösung gegen null konvergiert. Weiterhin wird ein Optimalsteuerungsproblem mit einem nicht-glatten L\(^1\)-Zielverfolgungsterm und einer nicht-glatten Zustandsgleichung untersucht. Für diesen Zweck wird eine adjungierte Gleichung definiert und das SQHVerfahren wird benutzt um das entsprechende Optimalsteuerungsproblem zu lösen. Der letzte Teil dieser Dissertation ist einer Klasse von FP Modellen gewidmet, die auf bestimmte stochastische Prozesse bezogen sind. Die Diskussion beginnt mit dem Fokus auf Random Walks bei dem auch Sprünge mit enthalten sind. Dieser Rahmen erlaubt die Herleitung eines diskreten FP Modells, das einem kontinuierlichen FP Modell mit Sprüngen und Randbedingungen entspricht, die sich zwischen absorbierend bis komplett reflektierend bewegen. Diese Diskussion erlaubt die Betrachtung der Driftsteuerung, die aus einer anisotropen Wahrscheinlichkeit für die Schritte des Random Walks resultiert. Danach werden zwei Drift-Diffusionsprozesse und die entsprechenden FP Modelle mit zwei verschiedenen Steuerungsstrategien für ein Optimalsteuerungsproblem mit Erwartungswertfunktional betrachtet. In der ersten Strategie hängen die Steuerungsfunktionen von der Zeit ab und in der zweiten hängen die Steuerungsfunktionen von Ort und Zeit ab. In beiden Fällen wird eine Lösung zum entsprechendem Optimalsteuerungsproblem mit den PMP Bedingungen charakterisiert, dargestellt in Satz 48 und Satz 49. Die Wohlgestelltheit des SQH Schemas ist in beiden Fällen gezeigt und weitere Bedingungen, die die Konvergenz des SQH Schemas zu einer PMP konsistenten Lösung sicherstellen, werden diskutiert. Der Fall einer Ort und Zeit abhängigen Steuerungsstrategie führt auf eine spezielle Struktur der entsprechenden PMP Bedingungen, die in einem weiteren Lösungsverfahren ausgenutzt werden, dem sogenannten direkten Hamiltonfunktionsverfahren (DH)

碩士
國立成功大學
化學工程研究所
81
The integral of the squared error is often used as a performance index in the design of control systems. The evaluation of ISE for systems having no delays can be easily accomplished by a parametric method which does not need to find the time response of the system. For systems with time delays, however, the evaluation of ISE is not an easy task. In this thesis, a direct numerical approach is presented to the evaluation of quadratic cost functionals for linear systems having multiple time delays. It is based on making use of the Parseval theorem and the bilinear transformation so that the computation of ISE involving time delays can be evaluated accurately and efficiently by means of a numerical integration method with automatic step-size adjustment. With this numerical algorithm of computing ISE, the following three control problems are solved: (1)Optimal reduced-order models with time delay: By representing the delay-free part of the reduced-order model in the Routh .gamma.-.delta. canonical form, the optimal parameters and the time delay are searched by an existing gradient-based method such that the ISE between the unit step responses of the system and model is minimized. (2)Design of an optimal PID controller satisfying prescribed gain and phase margins: The PID controller is find for a system such that the integral of the squared error of the closed-loop system subject to a unit step input is minimized, while satisfying the prescribed gain and phase margins. (3)Design of an optimal digital controller for sampled-data systems: With the integral of squared-error as the performance index, the parameters of the digital PID controller are searched to minimize the performance index.

碩士
國立臺北科技大學
機電整合研究所
93
This paper is to investigate the guaranteed cost control problem for a class of fuzzy uncertain singular time-delay systems. Based on the Tagaki-Sugeno fuzzy model and controller, the system can be locally linearlized. If we can find a special matrix which can transfer the singular problem into the normal system, then the associated robust stability condition is derived to ensure the robust quadratic stability of the system by using Lyapunov approach, and at the same time the upper bound of considered cost is found. In addition, the Linear Matrix Inequality (LMI) techniques are employed to solve the guaranteed cost problem. A fuzzy controller design algorithm is developed to stabilize the uncertain system and keep the cost at a certain level. Also, the method of finding observer-based dynamic output feedback controller is derived, and then the sufficient condition is transformed into a Linear Matrix Inequality (LMI) problem again. Observer-based control law can be obtained by solving two LMIs.

abstract: This thesis addresses the issue of making an economic case for energy storage in power systems. Bulk energy storage has often been suggested for large scale electric power systems in order to levelize load; store energy when it is inexpensive and discharge energy when it is expensive; potentially defer transmission and generation expansion; and provide for generation reserve margins. As renewable energy resource penetration increases, the uncertainty and variability of wind and solar may be alleviated by bulk energy storage technologies. The quadratic programming function in MATLAB is used to simulate an economic dispatch that includes energy storage. A program is created that utilizes quadratic programming to analyze various cases using a 2010 summer peak load from the Arizona transmission system, part of the Western Electricity Coordinating Council (WECC). The MATLAB program is used first to test the Arizona test bed with a low level of energy storage to study how the storage power limit effects several optimization out-puts such as the system wide operating costs. Very high levels of energy storage are then added to see how high level energy storage affects peak shaving, load factor, and other system applications. Finally, various constraint relaxations are made to analyze why the applications tested eventually approach a constant value. This research illustrates the use of energy storage which helps minimize the system wide generator operating cost by "shaving" energy off of the peak demand.
Dissertation/Thesis
M.S. Electrical Engineering 2013

Numerous advantages attained by integrating Distributed Generation (DG) in distribution systems. These advantages include decreasing power losses and improving voltage profiles. Such benefits can be achieved and enhanced if DGs are optimally sized and located in the systems. In this thesis, the optimal DG placement and sizing problem is investigated using two approaches. First, the optimization problem is treated as single-objective optimization problem, where the system’s active power losses are considered as the objective to be minimized. Secondly, the problem is tackled as a multi-objective one, focusing on DG installation costs. These problems are formulated as constrained nonlinear optimization problems using the Sequential Quadratic Programming method. A weighted sum method and a fuzzy decision-making method are presented to generate the Pareto optimal front and also to obtain the best compromise solution. Single and multiple DG installation cases are studied and compared to a case without DG, and a 15-bus radial distribution system and 33-bus meshed distribution system are used to demonstrate the effectiveness of the proposed methods.