Publication:
Consistent approximation of a nonlinear optimal control problem with uncertain parameters

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Authors
Phelps, Chris
Gong, Qi
Royset, Johannes O.
Walton, Claire
Kaminer, Isaac
Subjects
Optimal control
Computational methods
Optimization
Nonlinear system
Search theory
Advisors
Date of Issue
2014
Date
Publisher
Elsevier
Language
Abstract
This paper focuses on a non-standard constrained nonlinear optimal control problem in which the objective functional involves an integration over a space of stochastic parameters as well as an integration over the time domain. The research is inspired by the problem of optimizing the trajectories of multiple searchers attempting to detect non-evading moving targets. In this paper, we propose a framework based on the approximation of the integral in the parameter space for the considered uncertain optimal control problem. The framework is proved to produce a zeroth-order consistent approximation in the sense that accumulation points of a sequence of optimal solutions to the approximate problem are optimal solutions of the original problem. In addition, we demonstrate the convergence of the corresponding adjoint variables. The accumulation points of a sequence of optimal state-adjoint pairs for the approximate problem satisfy a necessary condition of Pontryagin Minimum Principle type, which facilitates assessment of the optimality of numerical solutions.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1016/j.automatica.2014.10.025
Series/Report No
Department
Operations Research
Mechanical and Astronautical Engineering
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
This work is supported by US Office of Naval Research under Grant N0001412WX21229
Funder
Grant N0001412WX21229
Format
11 p.
Citation
Automatica, v. 50, 2014, pp. 2987-2997.
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.
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