Sample Average Approximations in Optimal Control of Uncertain Systems
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Authors
Royset, Johannes O.
Phelps, Chris
Gong, Qi
Subjects
Advisors
Date of Issue
2013-12
Date
December 2013
Publisher
IEEE
Language
Abstract
This paper focuses on an optimal control problem
in which the objective is to minimize the expectation of a
cost functional with stochastic parameters. The inclusion of the
stochastic parameters in the objective raises new theoretical and
computational challenges not present in a standard nonlinear
optimal control problem. In this paper, we provide a numerical
framework for the solution of this uncertain optimal control
problem by taking a sample average approximation approach.
An independent random sample is taken from the parameter
space, and the expectation is approximated by the sample
average. The result is a family of standard nonlinear optimal
control problems which can be solved using existing techniques.
We provide an optimality function for both the uncertain
optimal control problem and its approximation, and show that
the approximation based on the sample average approach is
consistent in the sense of Polak. We illustrate the approach with
a numerical example arising in optimal search for a moving
target.
Type
Conference Paper
Description
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Office of Naval Research grant N0001412WX21229
Funder
Office of Naval Research grant N0001412WX21229
Format
8 p.
Citation
C. Phelps, J.O. Royset, and Q. Gong, 2013, "Sample average approximations in optimal control of uncertain systems," in Proceedings of the 51st IEEE Conference on Decision and Control (CDC 2013), Florence, Italy.
Distribution Statement
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.