A weak Hamiltonian finite element method for optimal control problemsA 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.
Document ID
19910043965
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Hodges, Dewey H. (Georgia Inst. of Tech. Atlanta, GA, United States)
Bless, Robert R. (Georgia Institute of Technology Atlanta, United States)
Date Acquired
August 14, 2013
Publication Date
January 1, 1990
Subject Category
Cybernetics
Meeting Information
Meeting: Southeastern Conference on Theoretical and Applied Mechanics