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Successive Galerkin approximation of nonlinear optimal attitude

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3 Author(s)
J. R. Lawton ; Dept. of Electr. & Comput. Eng., Brigham Young Univ., Provo, UT, USA ; R. W. Beard ; T. W. Mclain

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

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American Control Conference, 1999. Proceedings of the 1999  (Volume:6 )

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