Restoration algorithm for solving optimal control problems with nondifferential constraints and general boundary conditions

Simple item page
dc.contributor.advisorMiele, Angeloen_US
dc.contributor.committeeMemberBayazitoglu, Yildizen_US
dc.contributor.committeeMemberThrall, Robert M.en_US
dc.creatorHuang, G. T. C.en_US
dc.date.accessioned2018-12-18T21:29:31Zen_US
dc.date.available2018-12-18T21:29:31Zen_US
dc.date.issued1981en_US
dc.description.abstractThis thesis considers the numerical solution of the problem of minimizing a functional I, subject to differential constraints, non-differential constraints, and general boundary conditions. It consists of finding the state x(t), the control u(t), and the parameter pi, so that the functional is minimized, while the constraints are satisfied to a predetermined accuracy. First, a new version of the restoration algorithm is developed, in order to solve the following sub-problem: find a feasible solution, starting from a non-feasible solution. This task is accomplished in a cycle, composed of several restorative iterations. In each restorative iteration, variations of the state, the control, and the parameter are produced so as to achieve first-order constraint satisfaction, while minimizing the norm squared of the variations of the control and the parameter. Next, a transformation technique is employed. By proper augmentation of the state vector and the parameter vector, and by proper redefinition of the constraining relations, a transformed system is obtained. In this transformed system, the value of the functional I becomes a component of the augmented parameter. Then, the original minimization problem is replaced by the problem of finding the smallest value of the parameter I for which the transformed system admits a feasible solution. In this connection, ways and means are explored for approaching the minimum of the parameter I by cyclical application of the restoration algorithm. As a whole, the minimization algorithm is composed of a sequence of restorative cycles. Two consecutive elements of the sequence are such that the value of the parameter I at the end of any cycle is smaller than the value of the parameter I at the end of the previous cycle. The driving force which enables the restoration algorithm to continue is the lowering of the value of parameter I after a feasible solution has been obtained. This supplies the disturbance necessary for the restoration algorithm to continue. Depending on the strategy employed for the driving parameter and the strategy employed for the error in the feasibility equations, different versions of the minimization algorithm are developed: Algorithms A1, A2, A3 and Algorithms B1, B2, B3. These versions are tested through four numerical examples, and it is found that they perform in a satisfactory way. Thus, the numerical results show the feasibility as well as the convergence characteristics of the present algorithm.en_US
dc.format.digitalOriginreformatted digitalen_US
dc.format.extent57 ppen_US
dc.identifier.callnoThesis Math. Sci. 1981 Huangen_US
dc.identifier.citationHuang, G. T. C.. "Restoration algorithm for solving optimal control problems with nondifferential constraints and general boundary conditions." (1981) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104728">https://hdl.handle.net/1911/104728</a>.en_US
dc.identifier.digitalRICE2364en_US
dc.identifier.urihttps://hdl.handle.net/1911/104728en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.titleRestoration algorithm for solving optimal control problems with nondifferential constraints and general boundary conditionsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
RICE2364.pdf
Size:
1.06 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations