"An algorithm based on the mechanics of natural genetics is used to solve two different optimization problems. The algorithm combines survival of the fittest among string structures with randomized information exchange to form a search algorithm. Initiated with a population of bits-coded individuals, the genetic algorithm searches for the optimal solutions generation-by-generation. The three main operations in the genetic algorithm: Reproduction, Crossover, and Mutation give this algorithm the power of searching. In the first part of this thesis, the genetic algorithm is used to determine the optimal trajectories of the aeroassisted vehicle reentry problem. The trajectories to be optimized are determined not only by the parameter searching but also under a height constraint which make this study more interesting. In the second part of this thesis the genetic algorithm is used for designing three-axis bang-bang controllers for the time-optimal rigid spacecraft reorientation problem. The firing times of the bang-bang controller and the time of rotation are determined by searching for the angular velocity thresholds and the reorientation time"--Abstract, leaf iv.
This book explores the design of optimal trajectories for space maneuver vehicles (SMVs) using optimal control-based techniques. It begins with a comprehensive introduction to and overview of three main approaches to trajectory optimization, and subsequently focuses on the design of a novel hybrid optimization strategy that combines an initial guess generator with an improved gradient-based inner optimizer. Further, it highlights the development of multi-objective spacecraft trajectory optimization problems, with a particular focus on multi-objective transcription methods and multi-objective evolutionary algorithms. In its final sections, the book studies spacecraft flight scenarios with noise-perturbed dynamics and probabilistic constraints, and designs and validates new chance-constrained optimal control frameworks. The comprehensive and systematic treatment of practical issues in spacecraft trajectory optimization is one of the book’s major features, making it particularly suited for readers who are seeking practical solutions in spacecraft trajectory optimization. It offers a valuable asset for researchers, engineers, and graduate students in GNC systems, engineering optimization, applied optimal control theory, etc.
This book focuses on the design and application of advanced trajectory optimization and guidance and control (G&C) techniques for aerospace vehicles. Part I of the book focuses on the introduction of constrained aerospace vehicle trajectory optimization problems, with particular emphasis on the design of high-fidelity trajectory optimization methods, heuristic optimization-based strategies, and fast convexification-based algorithms. In Part II, various optimization theory/artificial intelligence (AI)-based methods are constructed and presented, including dynamic programming-based methods, model predictive control-based methods, and deep neural network-based algorithms. Key aspects of the application of these approaches, such as their main advantages and inherent challenges, are detailed and discussed. Some practical implementation considerations are then summarized, together with a number of future research topics. The comprehensive and systematic treatment of practical issues in aerospace trajectory optimization and guidance and control problems is one of the main features of the book, which is particularly suitable for readers interested in learning practical solutions in aerospace trajectory optimization and guidance and control. The book is useful to researchers, engineers, and graduate students in the fields of G&C systems, engineering optimization, applied optimal control theory, etc.
Masters Theses in the Pure and Applied Sciences was first conceived, published, and disseminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS)* at Purdue University in 1957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dis semination phases of the activity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thought that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all concerned if the printing and distribution of the volumes were handled by an international publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Corporation of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 39 (thesis year 1994) a total of 13,953 thesis titles from 21 Canadian and 159 United States universities. We are sure that this broader base for these titles reported will greatly enhance the value of this impor tant annual reference work. While Volume 39 reports theses submitted in 1994, on occasion, certain uni versities do report theses submitted in previous years but not reported at the time.
Evolutionary algorithms can be used to solve interesting problems for aeronautical and astronautical applications, and it is a must to review the fundamentals of the most common evolutionary algorithms being used for those applications. Genetic algorithms, particle swarm optimization, firefly algorithm, ant colony optimization, artificial bee colony optimization, and the cuckoo search algorithm are presented and discussed with an emphasis on astronautical applications. In summary, the genetic algorithm and its variants can be used for a large parameter space but is more efficient in global optimization using a smaller chromosome size such that the number of parameters being optimized simultaneously is less than 1000. It is found that PID controller parameters, nonlinear parameter identification, and trajectory optimization are applications ripe for the genetic algorithm. Ant colony optimization and artificial bee colony optimization are optimization routines more suited for combinatorics, such as with trajectory optimization, path planning, scheduling, and spacecraft load bearing. Particle swarm optimization, firefly algorithm, and cuckoo search algorithms are best suited for large parameter spaces due to the decrease in computation need and function calls when compared to the genetic algorithm family of optimizers. Key areas of investigation for these social evolution algorithms are in spacecraft trajectory planning and in parameter identification.
The optimization of spacecraft trajectories has been, and continues to be, critical for the development of modern space missions. Longer flight times, continuous low-thrust propulsion, and multiple flybys are just a few of the modern features resulting in increasingly complex optimal control problems for trajectory designers to solve. In order to efficiently tackle such challenging problems, a variety of methods and algorithms have been developed over the last decades. The work presented in this dissertation aims at improving the solutions and the robustness of the optimal control algorithms, in addition to reducing their computational load and the amount of necessary human involvement. Several areas of improvement are examined in the dissertation. First, the general formulation of a Differential Dynamic Programming (DDP) algorithm is examined, and new theoretical developments are made in order to achieve a multiple-shooting formulation of the method. Multiple-shooting transcriptions have been demonstrated to be beneficial to both direct and indirect optimal control methods, as they help decrease the large sensitivities present in highly nonlinear problems (thus improving the algorithms' robustness), and increase the potential for a parallel implementation. The new Multiple-Shooting Differential Dynamic Programming algorithm (MDDP) is the first application of the well-known multiple-shooting principles to DDP. The algorithm uses a null-space trust-region method for the optimization of quadratic subproblems subject to simple bounds, which permits to control the quality of the quadratic approximations of the objective function. Equality and inequality path and terminal constraints are treated with a general Augmented Lagrangian approach. The choice of a direct transcription and of an Augmented Lagrangian merit function, associated with automated partial computations, make the MDDP implementation flexible, requiring minimal user effort for changes in the dynamics, cost and constraint functions. The algorithm is implemented in a general, modular optimal control software, and the performance of the multiple-shooting formulation is analyzed. The use of quasi-Newton approximations in the context of DDP is examined, and numerically demonstrated to improve computational efficiency while retaining attractive convergence properties. The computational performance of an optimal control algorithm is closely related to that of the integrator chosen for the propagation of the equation of motion. In an effort to improve the efficiency of the MDDP algorithm, a new numerical propagation method is developed for the Kepler, Stark, and three-body problems, three of the most commonly used dynamical models for spacecraft trajectory optimization. The method uses a time regularization technique, the generalized Sundman transformation, and Taylor Series developments of equivalents to the f and g functions for each problem. The performance of the new method is examined, and specific domains where the series solution outperforms existing propagation methods are identified. Finally, because the robustness and computational efficiency of the MDDP algorithm depend on the quality of the first- and second-order State Transition Matrices, the three most common techniques for their computation are analyzed, in particular for low-fidelity propagation. The propagation of variational equations is compared to the complex step derivative approximation and finite differences methods, for a variety of problems and integration techniques. The subtle differences between variable- and fixed-step integration for partial computation are revealed, common pitfalls are observed, and recommendations are made for the practitioner to enhance the quality of state transition matrices.
