Galerkin approximation, Isaacs equation
The successive Galerkin approximation (SGA) algorithm has recently been developed for approximating solutions to the Hamilton-Jacobi-Isaacs equation. The algorithm produces feedback control laws that are stabilizing on a well-defined region of state space. The objective of this paper is to demonstrate the application of the SGA algorithm to two simple examples. The examples serve several purposes: first they illustrate how the algorithm is applied in a setting that is simple enough to write out in detail, second they demonstrate the convergence of the algorithm in a setting where the actual solution can be derived analytically.
Original Publication Citation
Beard, R., McLain, T., and Wen, J. Successive Galerkin Approximation of the Isaacs Equation, Proceedings of the 14th IFAC World Congress, no. 5, pp. 717-743, July 1999, Beijing, China.
BYU ScholarsArchive Citation
McLain, Timothy; Beard, Randal W.; and Wen, John T., "Successive Galerkin Approximation of the Isaacs Equation" (1999). All Faculty Publications. 1938.
Ira A. Fulton College of Engineering and Technology
Copyright © 1999 International Federation of Automatic Control. Published by Elsevier Ltd. All rights reserved. This is the author's submitted version of this article. The definitive version can be found at http://www.sciencedirect.com/science/article/pii/S147466701756351X
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