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Full-Text Articles in Engineering
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 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.
Nonlinear Optimal Control Of A Hydraulically Actuated Positioning System, Timothy Mclain, Randal W. Beard
Nonlinear Optimal Control Of A Hydraulically Actuated Positioning System, Timothy Mclain, Randal W. Beard
Faculty Publications
In this paper, the nonlinear optimal control problem is formulated for the position control of an electrohydraulic servo system. The optimal control is given by the solution to the Hamilton-Jacobi-Bellman equation, which in this case cannot be solved explicitly. An alternative method, based upon successive Galerkin approximation, is used to obtain an approximate optimal solution. Preliminary simulation results, demonstrating the application of this approach to the position control of a hydraulically actuated device, are presented.