Pseudospectral Methods for Infinite-Horizon Optimal Control Problems
Ross, Michael I.
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A central computational issue in solving infinite-horizon nonlinear optimal control problems is the treatment of the horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of pseudospectral methods. Although any pseudospectral method may be used, we focus on the Legendre pseudospectral method. It is shown that the proper class of Legendre pseudospectral methods to solve infinitehorizon problems are the Radau-based methods with weighted interpolants. This is in sharp contrast to the unweighted pseudospectral techniques for optimal control. The Legendre–Gauss–Radau pseudospectral method is thus developed to solve nonlinear constrained optimal control problems. An application of the covector mapping principle for the Legendre–Gauss–Radau pseudospectral method generates a covector mapping theorem that provides an efficient approach for the verification and validation of the extremality of the computed solution. Several example problems are solved to illustrate the ideas.
The article of record as published may be found at http://dx.doi.org/10.2514/1.33117
RightsThis 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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Fahroo, Fariba; Ross, I. Michael (The American Institute of Aeronautics and Astronautics (AIAA), 2008-08-18);Recently, the Legendre Pseudospectral (PS) method migrated from theory to fight application onboard the International Space Station for performing a finite-horizon, zero- propellant maneuver. A small technical modification ...
Fahroo, Fariba; Ross, I. Michael (The American Institute of Aeronautics and Astronautics (AIAA), 2006-08-21);One of the most efficient families of techniques for solving space trajectory optimization problems are pseudospectral (PS) methods. Among the rich variety of PS methods, the class of Legendre PS methods are most thoroughly ...
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