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With the rapid growth of space activities and advancement of aerospace science and technology, many autonomous space missions have been proliferating in recent decades. Control of spacecraft in proximity operations is of great importance to accomplish these missions. The research in this dissertation aims to provide a precise, efficient, optimal, and robust controller to ensure successful spacecraft proximity operations. This is a challenging control task since the problem involves highly nonlinear dynamics including translational motion, rotational motion, and flexible structure deformation and vibration. In addition, uncertainties in the system modeling parameters and disturbances make the precise control more difficult. Four control design approaches are integrated to solve this challenging problem. The first approach is to consider the spacecraft rigid body translational and rotational dynamics together with the flexible motion in one unified optimal control framework so that the overall system performance and constraints can be addressed in one optimization process. The second approach is to formulate the robust control objectives into the optimal control cost function and prove the equivalency between the robust stabilization problem and the transformed optimal control problem. The third approach is to employ the è-D technique, a novel optimal control method that is based on a perturbation solution to the Hamilton-Jacobi-Bellman equation, to solve the nonlinear optimal control problem obtained from the indirect robust control formulation. The resultant optimal control law can be obtained in closedorm, and thus facilitates the onboard implementation. The integration of these three approaches is called the integrated indirect robust control scheme. The fourth approach is to use the inverse optimal adaptive control method combined with the indirect robust control scheme to alleviate the conservativeness of the indirect robust control scheme by using online parameter estimation such that adaptive, robust, and optimal properties can all be achieved. To show the effectiveness of the proposed control approaches, six degree-offreedom spacecraft proximity operation simulation is conducted and demonstrates satisfying performance under various uncertainties and disturbances.

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In this dissertation we focus on fractional-order dynamical systems and classify these problems as optimal control of system described by fractional derivative, fractional-order nonlinear differential equations, optimal control of systems described by variable-order differential equations and delay fractional optimal control problems. These problems are solved by using the spectral method and reducing the problem to a system of algebraic equations. In fact for the optimal control problems described by fractional and variable-order equations, the variables are approximated by chosen wavelets with unknown coefficients in the constraint equations, performance index and conditions. Thus, a fractional optimal control problem is converted to an optimization problem, which can be solved numerically. We have applied the new generalized wavelets to approximate the fractional-order nonlinear differential equations such as Riccati and Bagley-Torvik equations. Then, the solution of this kind of problem is found using the collocation method. For solving the fractional optimal control described by fractional delay system, a new set of hybrid functions have been constructed. Also, a general and exact formulation for the fractional-order integral operator of these functions has been achieved. Then we utilized it to solve delay fractional optimal control problems directly. The convergence of the present method is discussed. For all cases, some numerical examples are presented and compared with the existing results, which show the efficiency and accuracy of the present method.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24266号 / 情博第810号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科システム科学専攻 / (主査)教授 大塚 敏之, 教授 石井 信, 教授 森本 淳 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Single particle tracking has become a ubiquitous class of tools in the study of biology at the molecular level. While the broad adoption of these techniques has yielded significant advances, it has also revealed the limitations of the methods. Most notable among these is that traditional single particle tracking is limited to imaging the particle at low temporal resolutions and small axial ranges. This restricts applications to slow processes confined to a plane. Biological processes in the cell, however, happen at multiple time scales and length scales. Real-time feedback-driven single particle tracking microscopes have emerged as one group of methods that can overcome these limitations. However, the development of these techniques has been ad-hoc and their performance has not been consistently analyzed in a way that enables comparisons across techniques, leading to incremental improvements on existing sets of tools, with no sense of fit or optimality with respect to SPT experimental requirements. This thesis addresses these challenges through three key questions : 1) What performance metrics are necessary to compare different techniques, allowing for easy selection of the method that best fits a particular application? 2) What is a procedure to design single particle tracking microscopes for the best performance?, and 3) How does one controllably and repeatably experimentally test single particle tracking performance on specific microscopes?. These questions are tackled in four thrusts: 1) a comprehensive review of real-time feedback-driven single particle tracking spectroscopy, 2) the creation of an optimization framework using Fisher information, 3) the design of a real-time feedback-driven single particle tracking microscope utilizing extremum seeking control, and 4) the development of synthetic motion, a protocol that provides biologically relevant known ground-truth particle motion to test single particle tracking microscopes and data analysis algorithms. The comprehensive review yields a unified view of single particle tracking microscopes and highlights two clear challenges, the photon budget and the control temporal budget, that work to limit the two key performance metrics, tracking duration and Fisher information. Fisher information provides a common framework to understand the elements of real-time feedback-driven single particle tracking microscopes, and the corresponding information optimization framework is a method to optimally design these microscopes towards an experimental aim. The thesis then expands an existing tracking algorithm to handle multiple particles through a multi-layer control architecture, and introduces REACTMIN, a new approach that reactively scans a minimum of light to overcome both the photon budget and the control temporal budget. This enables tracking durations up to hours, position localization down to a few nanometers, with temporal resolutions greater than 1 kHz. Finally, synthetic motion provides a repeatable and programmable method to test single particle tracking microscopes and algorithms with a known ground truth experiment. The performance of this method is analyzed in the presence of common actuator limitations. / 2024-01-16T00:00:00Z

<p> The dual configuration is innovated as a new approach in sensitivity reduction. Three types of sensitivity due to variations in plant parameters are discussed. It has been shown that cost insensitive and terminal insensitive designs are indeed achievable by applying the dual configuration to implement the optimal control. </p> <p> The theory has been developed for a general class of optimal systems and the linear systems with quadratic cost functionals have been analytically evaluated to illustrate the theory. </p> / Thesis / Master of Engineering (ME)