nonlinear optimal control, attitude control, Galerkin approximation
This paper presents the application of the successive Galerkin approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkin's method approximates the value function by a truncated Galerkin series expansion. To do so, a truncated Galerkin basis set is formed. A sufficient number of functions must be included in this Galerkin basis set in order to guarantee that the solution will be a stabilizing control. By increasing the size of the Galerkin basis the quality of the approximation is improved at the cost of rapid growth in the computation load of the SGA. A major result of this paper is the development of the Galerkin basis set in the context of the optimal attitude control problem.
Original Publication Citation
Lawton, J., Beard, R., and McLain, T. Successive Galerkin Approximation of a Nonlinear Optimal Attitude Control, Proceedings of the American Control Conference, vol. 6, pp. 4373-4377, June 1999, San Diego, California.
BYU ScholarsArchive Citation
McLain, Timothy; Beard, Randal W.; and Lawton, Johnathan, "Successive Galerkin Approximation of a Nonlinear Optimal Attitude Control" (1999). Faculty Publications. 1937.
Ira A. Fulton College of Engineering and Technology
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