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Record 24 of 430
A weak Hamiltonian finite element method for optimal control problems
Author and Affiliation:
Hodges, Dewey H.(Georgia Inst. of Tech., Atlanta, GA, United States)
Bless, Robert R.(Georgia Institute of Technology, Atlanta, United States)
Abstract: A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Publication Date: Jan 01, 1990
Document ID:
19910043965
(Acquired Nov 28, 1995)
Accession Number: 91A28588
Subject Category: CYBERNETICS
Document Type: Conference Paper
Publication Information: (SEE A91-28576)
Publisher Information: United States
Meeting Information: Southeastern Conference on Theoretical and Applied Mechanics; Mar 22-23, 1990; Atlanta, GA; United States
Contract/Grant/Task Num: NAG1-939
Financial Sponsor: NASA; United States
Organization Source: Georgia Inst. of Tech.; Atlanta, GA, United States
Description: 8p; In English
Distribution Limits: Unclassified; Publicly available; Unlimited
Rights: Copyright
NASA Terms: CLASSICAL MECHANICS; DYNAMICAL SYSTEMS; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; HAMILTONIAN FUNCTIONS; OPTIMAL CONTROL; TIME MARCHING; TRAJECTORY OPTIMIZATION; VARIATIONAL PRINCIPLES; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; MOMENTUM; PENDULUMS
Imprint And Other Notes: IN: Developments in theoretical and applied mechanics. Vol. 15 - Proceedings of the 15th Southeastern Conference on Theoretical and Applied Mechanics, Atlanta, GA, Mar. 22, 23, 1990 (A91-28576 11-31). Atlanta, GA, Georgia Institute of Technology, 1990, p. 171-178. Previously announced in STAR as N89-24873.
Availability Source: Other Sources
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