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Full-Text Articles in Mechanical 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 …
Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard
Successive Galerkin Approximation Algorithms For Nonlinear Optimal And Robust Control, Timothy Mclain, Randal W. Beard
Faculty Publications
Nonlinear optimal control and nonlinear H infinity control are two of the most significant paradigms in nonlinear systems theory. Unfortunately, these problems require the solution of Hamilton-Jacobi equations, which are extremely difficult to solve in practice. To make matters worse, approximation techniques for these equations are inherently prone to the so-called 'curse of dimensionality'. While there have been many attempts to approximate these equations, solutions resulting in closed-loop control with well-defined stability and robustness have remained elusive. This paper describes a recent breakthrough in approximating the Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations. Successive approximation and Galerkin approximation methods are combined to derive …
Successive Galerkin Approximations To The Nonlinear Optimal Control Of An Underwater Robotic Vehicle, Timothy Mclain, Randal W. Beard
Successive Galerkin Approximations To The Nonlinear Optimal Control Of An Underwater Robotic Vehicle, Timothy Mclain, Randal W. Beard
Faculty Publications
The application of a new nonlinear optimal control strategy to the station-keeping control of an underwater robotic vehicle is considered. The control approach described and demonstrated here is based upon the numerical approximation of solutions to the Hamilton-Jacobi-Bellman equation. These solutions are computed by an iterative application of Galerkin's method. Preliminary simulation results demonstrating the application of this approach to the control of an underwater vehicle in the horizontal plane are presented.