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Full-Text Articles in Engineering
Nonlinear Robust Missile Autopilot Design Using Successive Galerkin Approximation, Timothy Mclain, Randal W. Beard
Nonlinear Robust Missile Autopilot Design Using Successive Galerkin Approximation, Timothy Mclain, Randal W. Beard
Faculty Publications
The application of a new nonlinear robust control strategy to the design of missile autopilots is presented. The control approach described and demonstrated here is based upon the numerical solution of the Hamilton-Jacobi-Isaacs equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Application of this approach to the design of a pitch-axis autopilot for a missile having uncertain pitch moment and lift force is described.
Successive Galerkin Approximation Of The Isaacs Equation, Timothy Mclain, Randal W. Beard, John T. Wen
Successive Galerkin Approximation Of The Isaacs Equation, Timothy Mclain, Randal W. Beard, John T. Wen
Faculty Publications
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.
Successive Galerkin Approximation Of A Nonlinear Optimal Attitude Control, Timothy Mclain, Randal W. Beard, Johnathan Lawton
Successive Galerkin Approximation Of A Nonlinear Optimal Attitude Control, Timothy Mclain, Randal W. Beard, Johnathan Lawton
Faculty Publications
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 …