The design of optimal strictly positive real (SPR) compensators using numerical optimization is considered. The plants to be controlled are linear and nonlinear flexible manipulators. For the design of SISO and MIMO linear SPR controllers, the optimization objective function is defined by reformulating the H2-optimal control problem subject to the constraint that the controllers must be SPR. Various controller parameterizations using transfer functions/matrices and state-space equations are considered. Depending on the controller form, constraints are enforced (i) using simple inequalities guaranteeing SPRness, (ii) in the frequency domain, or (iii) by implementing the Kalman-Yakubovich- Popov lemma. The design of a gain-scheduled SPR controller using numerical optimization is also considered. Using a family of linear SPR controllers, the time dependent scheduling signals are parameterized, and the objective function of the optimizer seeks to find the form of the scheduling signals which minimizes the manipulator tip tracking error while minimizing the control effort.

Non-planar lifting surfaces offer potentially significant gains in aerodynamic efficiency by lowering induced drag. Non-aerodynamic considerations, such as structures can impact the overall efficiency. Here, a panel method and equivalent beam finite element model are used to explore non-planar configurations taking into account the coupling between aerodynamics and structures. A single discipline aerodynamic optimization and a multidisciplinary aerostructural optimization are investigated. Due to the complexity of the design space and the presence of multiple local minima, an augmented Lagrangian particle swarm optimizer is used. The aerodynamic optimum solution found for rectangular lifting surfaces is a box wing, while allowing for sweep and taper yields a joined wing. Adding parasitic drag in the aerodynamic model reduces the size of the non--planar elements. The aerostructural optimal solution found is a winglet configuration when the span is constrained and a wing rake when there is no such constraint.

The release of flammable and toxic chemicals in petrochemical facilities is a major concern when designing modern process safety systems. While the proper selection of the necessary types of gas detectors needed is important, appropriate placement of these detectors is required in order to have a well-functioning gas detection system. However, the uncertainty in leak locations, gas composition, process and weather conditions, and process geometries must all be considered when attempting to determine the appropriate number and placement of the gas detectors. Because traditional approaches are typically based on heuristics, there exists the need to develop more rigorous optimization based approaches to handling this problem. This work presents several mixed-integer programming formulations to address this need. First, a general mixed-integer linear programming problem is presented. This formulation takes advantage of precomputed computational fluid dynamics (CFD) simulations to determine a gas detector placement that minimizes the expected detection time across all scenarios. An extension to this formulation is added that considers the overall coverage in a facility in order to improve the detector placement when enough scenarios may not be available. Additionally, a formulation considering the Conditional-Value-at-Risk is also presented. This formulation provides some control over the shape of the tail of the distribution, not only minimizing the expected detection time across all scenarios, but also improving the tail behavior. In addition to improved formulations, procedures are introduced to determine confidence in the placement generated and to determine if enough scenarios have been used in determining the gas detector placement. First, a procedure is introduced to analyze the performance of the proposed gas detector placement in the face of “unforeseen” scenarios, or scenarios that were not necessarily included in the original formulation. Additionally, a procedure for determine the confidence interval on the optimality gap between a placement generated with a sample of scenarios and its estimated performance on the entire uncertainty space. Finally, a method for determining if enough scenarios have been used and how much additional benefit is expected by adding more scenarios to the optimization is proposed. Results are presented for each of the formulations and methods presented using three data sets from an actual process facility. The use of an off-the-shelf toolkit for the placement of detectors in municipal water networks from the EPA, known as TEVA-SPOT, is explored. Because this toolkit was not designed for placing gas detectors, some adaptation of the files is necessary, and the procedure for doing so is presented.

Semidefinite programming is a powerful modeling tool for a wide range of optimization and feasibility problems. Its prevalent use in practice relies on the fact that a (nearly) optimal solution of a semidefinite program can be obtained efficiently in both theory and practice, provided that the semidefinite program and its dual satisfy the Slater condition. This thesis focuses on the situation where the Slater condition (i.e., the existence of positive definite feasible solutions) does not hold for a given semidefinite program; the failure of the Slater condition often occurs in structured semidefinite programs derived from various applications. In this thesis, we study the use of the facial reduction technique, originally proposed as a theoretical procedure by Borwein and Wolkowicz, as a preprocessing technique for semidefinite programs. Facial reduction can be used either in an algorithmic or a theoretical sense, depending on whether the structure of the semidefinite program is known a priori. The main contribution of this thesis is threefold. First, we study the numerical issues in the implementation of the facial reduction as an algorithm on semidefinite programs, and argue that each step of the facial reduction algorithm is backward stable. Second, we illustrate the theoretical importance of the facial reduction procedure in the topic of sensitivity analysis for semidefinite programs. Finally, we illustrate the use of facial reduction technique on several classes of structured semidefinite programs, in particular the side chain positioning problem in protein folding.

The current paradigm in the lens distortion characterization industry is to use simple radial distortion models with only one or two radial terms. Tangential terms and the optimal distortion centre are also seldom determined. Inherent in the models currently used is the assumption that lens distortion is radially symmetrical. The reason for the use of these models is partly due to the perceived instability of more complex lens distortion models. This dissertation shows, in the first of its three hypotheses, that higher order models are indeed beneficial, when their parameters are determined using modern numerical optimization techniques. They are both stable and provide superior characterization. Although it is true that the first two radial terms dominate the distortion characterization, this work proves superior characterization is possible for those applications that may require it. The third hypothesis challenges the assumption of the radial symmetry of lens distortion. Building on the foundation provided by the first hypothesis, a sample of lens distortion models of similar and greater complexity to those found in literature are modified to have a radial gain, allowing the distortion corrections to vary both with polar angle and distance from the distortion centre. Four angular gains are evaluated, and two provide better characterization. The elliptical gain was the only method to both consistently improve the characterization and not ‘skew’ the corrected images. This gain was shown to improve characterization by as much as 50% for simple (single radial term) models and by 7% for even the most complex models. To create an undistorted image from a distorted image captured through a lens which has had its distortion characterized, one needs to find the corresponding distorted pixel for each undistorted pixel in the corrected image. This is either done iteratively or using a simplified model typically based on the Taylor expansion of a simple (one or two radial coefficients) distortion model. The first method is accurate yet slow and the second, the opposite. The second hypothesis of this research successfully combines the advantages of both methods without any of their disadvantages. It was shown that, using the superior characterization of high order radial models (when fitted with modern numerical optimization methods) together with the ‘side-effect’ undistorted image points created in the lens distortion characterization, it is possible to fit a ‘reverse’ model from the undistorted to distorted domains. This reverse characterization is of similar complexity to the simplified models yet provides characterization equivalent to the iterative techniques. Compared to using simplified models the reverse mapping yields an improvement of more than tenfold - from the many tenths of pixels to a few hundredths. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22861号 / 情博第740号 / 新制||情||127(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 青柳 富誌生, 教授 磯 祐介, 教授 田口 智清 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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<p dir="ltr">This thesis presents a comprehensive exploration of advanced optimization strategies for addressing mixed-integer optimal control problems (MIOCPs) in aerospace applications, emphasizing the enhancement of convergence robustness, computational efficiency, and accuracy. The research develops a broad spectrum of optimization methodologies, including multi-phase approaches, parallel computing, reinforcement learning (RL), and distributed algorithms, to tackle complex MIOCPs characterized by highly nonlinear dynamics, intricate constraints, and discrete control variables.</p><p dir="ltr">Through discretization and reformulation, MIOCPs are transformed into general quadratically constrained quadratic programming (QCQP) problems, which are then equivalently converted into rank-one constrained semidefinite programs problems. To address these, iterative algorithms are developed specifically for solving such problems. Initially, two iterative search methods are introduced to achieve convergence: one is a hybrid alternating direction method of multipliers (ADMM) designed for large-scale QCQP problems, and the other is an iterative second-order cone programming (SOCP) algorithm developed to achieve global convergence. Moreover, to facilitate the convergence of these iterative algorithms and to enhance their solution quality, a multi-phase strategy is proposed. This strategy integrates with both the iterative ADMM and SOCP algorithms to optimize the solving of QCQP problems, improving both the convergence rate and the optimality of the solutions. To validate the effectiveness and improved computational performance of the proposed multi-phase iterative algorithms, the proposed algorithms were applied to several aerospace optimization problems, including six-degree-of-freedom (6-DoF) entry trajectory optimization, fuel-optimal powered descent, and multi-point precision landing challenges in a human-Mars mission. Theoretical analyses of convergence properties along with simulation results have been conducted, demonstrating the efficiency, robustness, and enhanced convergence rate of the optimization framework.</p><p dir="ltr">However, the iteration based multi-phase algorithms primarily guarantee only local optima for QCQP problems. This research introduces a novel approach that integrates a distributed framework with stochastic search techniques to overcome this limitation. By leveraging multiple initial guesses for collaborative communication among computation nodes, this method not only accelerates convergence but also enhances the exploration of the solution space in QCQP problems. Additionally, this strategy extends to tackle general nonlinear programming (NLP) problems, effectively steering optimization toward more globally promising directions. Numerical simulations and theoretical proofs validate these improvements, marking significant advancements in solving complex optimization challenges.</p><p dir="ltr">Following the use of multiple agents in QCQP problems, this research expand this advantage to address more general rank-constrained semidefinite programs (RCSPs). This research developed a method that decomposes matrices into smaller submatrices for parallel processing by multiple agents within a distributed framework. This approach significantly enhances computational efficiency and has been validated in applications such as image denoising, showcasing substantial improvements in both efficiency and effectiveness.</p><p dir="ltr">Moreover, to address uncertainties in applications, a learning-based algorithm for QCQPs with dynamic parameters is developed. This method creates high-performing initial guesses to enhance iterative algorithms, specifically applied to the iterative rank minimization (IRM) algorithm. Empirical evaluations show that the RL-guided IRM algorithm outperforms the original, delivering faster convergence and improved optimality, effectively managing the challenges of dynamic parameters.</p><p dir="ltr">In summary, this thesis introduces advanced optimization strategies that significantly enhance the resolution of MIOCPs and extends these methodologies to more general issues like NLP and RCSP. By integrating multi-phase approaches, parallel computing, distributed techniques, and learning methods, it improves computational efficiency, convergence, and solution quality. The effectiveness of these methods has been empirically validated and theoretically confirmed, representing substantial progress in the field of optimization.</p>

Increasing demands regarding performance, safety and environmental compatibility of hydraulic mobile machines in combination with rising cost pressures create a growing need for specialized optimization of hydraulic systems; particularly with regard to hydraulic reservoirs. In addition to the secondary function of cooling the oil, two main functions of the hydraulic reservoir are oil storage and de-aeration of the hydraulic oil. While designing hydraulic reservoirs regarding oil storage is quite simple, the design regarding de-aeration can be quite difficult. The author presents an approach to a system optimization of hydraulic reservoirs which combines experimental and numerical techniques to resolve some challenges facing hydraulic tank design. Specialized numerical tools are used in order to characterize the de-aeration performance of hydraulic tanks. Further the simulation of heat transfer is used to study the cooling function of hydraulic tank systems with particular attention to plastic tank solutions. To accompany the numerical tools, experimental test rigs have been built up to validate the simulation results and to provide additional insight into the design and optimization of hydraulic tanks which will be presented as well.

Esta tese propõe um modelo de regeneração de energia metroviária, baseado no controle de paradas e partidas do trem ao longo de sua viagem, com o aproveitamento da energia proveniente da frenagem regenerativa no sistema de tração. O objetivo é otimizar o consumo de energia, promover maior eficiência, na perspectiva de uma gestão sustentável. Aplicando o Algoritmo Genético (GA) para obter a melhor configuração de tráfego dos trens, a pesquisa desenvolve e testa o Algoritmo de Controle de Tração para Regeneração de Energia Metroviária (ACTREM), usando a Linguagem de programação C++. Para analisar o desempenho do algoritmo de controle ACTREM no aumento da eficiência energética, foram realizadas quinze simulações da aplicação do ACTREM na linha 4 - Amarela do metrô da cidade de São Paulo. Essas simulações demonstraram a eficiência do ACTREM para gerar, automaticamente, os diagramas horários otimizados para uma economia de energia nos sistemas metroviários, levando em consideração as restrições operacionais do sistema, como capacidade máxima de cada trem, tempo total de espera, tempo total de viagem e intervalo entre trens. Os resultados mostram que o algoritmo proposto pode economizar 9,5% da energia e não provocar impactos relevantes na capacidade de transporte de passageiros do sistema. Ainda sugerem possíveis continuidades de estudos. / This thesis proposes a subway energy regeneration model, based on control stops and train departures throughout his trip, with the use of energy from the regenerative braking in the drive system. The goal is to optimize the power consumption, improve efficiency, in view of sustainable management. Applying Genetic Algorithm (GA) to get the better of the trains traffic configuration, the research develops and tests the Traction Control Algorithm for Subway Energy Regeneration (ACTREM), using the C ++ programming language. To analyze the performance of ACTREM control algorithm in enhancing energy efficiency, there were fifteen simulations of applying ACTREM on line 4 - Yellow subway in São Paulo. These simulations showed the ACTREM efficiency to generate automatically diagrams schedules optimized for energy savings in metro systems, taking into account the system\'s operational constraints such as maximum each train capacity, total wait time, total travel time and interval between trains. The results show that the proposed algorithm can save 9.5% of the energy and not cause significant impacts on the transportation system capacity passengers. Also suggest possible continuities studies.