Adjoint-based algorithms and numerical methods for sensitivity generation and optimization of large scale dynamic systems

This thesis presents advances in numerical methods for the solution of optimal control problems. In particular, the new ideas and methods presented in this thesis contribute to the research fields of structure-exploiting Newton-type methods for large scale nonlinear programming and sensitivity generation for IVPs for ordinary differential equations and differential algebraic equations. Based on these contributions, a new lifted adjoint-based partially reduced exact-Hessian SQP (L-PRSQP) method for nonlinear multistage constrained optimization problems with large scale differential algebraic process models is proposed. It is particularly well suited for optimization problems which involve many state variables in the dynamic process but only few degrees of freedom, i.e., controls, parameter or free initial values. This L-PRSQP method can be understood as an extension of the work of Schäfer to the case of exact-Hessian SQP methods, making use of directional forward/adjoint sensitivities of second order. It stands hence in the tradition of the direct multiple shooting approaches for differential algebraic equations of index 1 of Bock and co-workers. To the novelties that are presented in this thesis further belong - the generalization of the direct multiple shooting idea to structure-exploiting algorithms for NLPs with an internal chain structure of the problem functions, - an algorithmic trick that allows these so-called lifted methods to compute the condensed subproblems directly based on minor modifications to the user given problem functions and without further knowledge on the internal structure of the problem, - a lifted adjoint-based exact-Hessian SQP method that is shown to be equivalent to a full-space approach, but only has the complexity of an unlifted/single shooting approach per iteration, - new adjoint schemes for sensitivity generation based on Internal Numerical Differentiation (IND) for implicit LMMs using the example of Backward Differentiation Formulas (BDF), - the combination of univariate Taylor coefficient (TC) propagation and IND, resulting in IND-TC schemes which allow for the first time the efficient computation of directional forward and forward/adjoint sensitivities of arbitrary order, - a strategy to propagate directional sensitivities of arbitrary order across switching events in the integration, - a local error control strategy for sensitivities and a heuristic global error estimation strategy for IVP solutions in connection with IND schemes, - the software packages DAESOL-II and SolvIND, implementing the ideas related to IVP solution and sensitivity generation, as well as the software packages LiftOpt and DynamicLiftOpt that implement the lifted Newton-type methods for general NLP problems and the L-PRSQP method in the optimal control context, respectively. The performance of the presented approaches is demonstrated by the practical application of our codes to a series of numerical test problems and by comparison to the performance of alternative state-of-the-art approaches, if applicable. In particular, the new lifted adjoint-based partially reduced exact-Hessian SQP method allows the efficient and successful solution of a practical optimal control problem for a binary distillation column, for which the solution using a direct multiple shooting SQP method with an exact-Hessian would have been prohibitively expensive until now

The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites

Aeronautical engineering: A continuing bibliography with indexes (supplement 289)

This bibliography lists 792 reports, articles, and other documents introduced into the NASA scientific and technical information system in Mar. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion