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Multigrid one shot methods for optimal control problems: Infinite dimensional controlThe multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.
Document ID
19950004411
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Arian, Eyal (Weizmann Inst. of Science Rehovoth, Israel)
Taasan, Shlomo (Weizmann Inst. of Science Rehovoth, Israel)
Date Acquired
September 6, 2013
Publication Date
July 1, 1994
Subject Category
Numerical Analysis
Report/Patent Number
NAS 1.26:194939
NASA-CR-194939
AD-A284376
ICASE-94-52
Accession Number
95N10823
Funding Number(s)
PROJECT: RTOP 505-90-52-01
CONTRACT_GRANT: NAS1-19480
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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