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Full-Text Articles in Mechanical Engineering
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.