An External Active-Set Strategy for Solving Optimal Control Problems
Elijah Polak, Hoam Chung and S. Shankar Sastry
EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2007-90
July 16, 2007
http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.pdf
We present a new, {\em external}, active constraints set strategy for solving nonlinear programming problems with a large number of inequality constraints that arise in the process of discretizing continuous-time optimal control problems with state-space constraints. This strategy constructs a sequence of inequality constrained nonlinear programming problems, containing a progressively larger subset of the constraints in the original problem, and submits them to a nonlinear programming solver for a fixed number of iterations. We prove that this scheme computes a solution of the original problem and show by means of numerical experiments that this strategy results in reductions in computing time ranging from a factor of 6 to a factor of over 100.
BibTeX citation:
@techreport{Polak:EECS-2007-90,
Author = {Polak, Elijah and Chung, Hoam and Sastry, S. Shankar},
Title = {An External Active-Set Strategy for Solving Optimal Control Problems},
Institution = {EECS Department, University of California, Berkeley},
Year = {2007},
Month = {Jul},
URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.html},
Number = {UCB/EECS-2007-90},
Abstract = {We present a new, {\em external}, active constraints
set strategy for solving nonlinear programming problems with a
large number of inequality constraints that arise in the process of
discretizing continuous-time optimal control problems with state-space
constraints. This strategy constructs a sequence of inequality constrained
nonlinear programming problems, containing a progressively larger
subset of the constraints in the original problem, and submits them to a
nonlinear programming solver for a fixed number of iterations. We prove
that this scheme computes a solution of the original problem and show by
means of numerical experiments that this strategy results in reductions
in computing time ranging from a factor of 6 to a factor of over 100.}
}
EndNote citation:
%0 Report %A Polak, Elijah %A Chung, Hoam %A Sastry, S. Shankar %T An External Active-Set Strategy for Solving Optimal Control Problems %I EECS Department, University of California, Berkeley %D 2007 %8 July 16 %@ UCB/EECS-2007-90 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2007/EECS-2007-90.html %F Polak:EECS-2007-90