Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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