Computational Methods in Optimal Control: Theory and Practice
About this ebook
Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge–Kutta methods.
Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer.
Computational Methods in Optimal Control: Theory and Practice is intended for numerical analysts and computational scientists. Users of the software package GPOPS may find the book useful since the theoretical basis for the GPOPS algorithm is developed within the book. It is appropriate for courses in variational analysis, numerical optimization, and the calculus of variations.
About the author
William W. Hager is a Distinguished Professor of Mathematics at the University of Florida and co-director of the Center for Applied Optimization. He has held positions at the University of South Florida, Carnegie Mellon University, and Penn State University. He is a Fellow of the Society for Industrial and Applied Mathematics. His research has focused on a convergence analysis for discrete approximations to problems in optimal control, and he has worked on the development of algorithms for solving the large sparse optimization problems that arise from the discretization of optimal control problems. He has also conducted research relating to the charge structure in thunderstorms. His estimator CONDEST for the 1-norm condition number of a matrix can be found in MATLAB.
