Successive Galerkin Approximation of Nonlinear Optimal Attitude Control
نویسندگان
چکیده
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 suucient 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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