Consistent approximation of an optimal search problem
Author
Phelps, Chris
Gong, Qi
Royset, Johannes O.
Kaminer, Isaac
Date
2012-12-10Metadata
Show full item recordAbstract
This paper focuses on the problem of optimizing
the trajectories of multiple searchers attempting to detect
a non-evading moving target whose motion is conditionally
deterministic. This problem is a parameter-distributed optimal
control problem, as it involves an integration over a space of
stochastic parameters as well as an integration over the time
domain. In this paper, we consider a wide range of discretization
schemes to approximate the integral in the parameter space
by a finite summation, which results in a standard controlconstrained
optimal control problem that can be solved using
existing techniques in optimal control theory. We prove that
when the sequence of solutions to the discretized problem has an
accumulation point, it is guaranteed to be an optimal solution
of the original search problem. We also provide a necessary
condition that accumulation points of this sequence must satisfy.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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