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Full-Text Articles in 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 …
Nonlinear Optimal Control Design Of A Missile Autopilot, Tim Mclain, Randal W. Beard
Nonlinear Optimal Control Design Of A Missile Autopilot, Tim Mclain, Randal W. Beard
Faculty Publications
The application of a new nonlinear optimal 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-Bellman equation by Successive Galerkin Approximation. Using this approach, feedback controllers are computed by an iterative application of a numerical Galerkin-type PDE solver. Simulation results demonstrating the application of this approach to the design of a missile autopilot are presented.
A Practical Algorithm For Designing H∞ Control Laws, Timothy Mclain, Randal W. Beard
A Practical Algorithm For Designing H∞ Control Laws, Timothy Mclain, Randal W. Beard
Faculty Publications
We describe an approximation method for the Hamilton-Jacobi-Isaacs (HJI) equation that results in feedback control. The approximation is accomplished via a two-step successive Galerkin approximation scheme. An application of the technique to the control of the forward motion of an underwater vehicle is described.