Some Aspects Of The Optimal Control Of Distributed Parameter Systems Based On Lectures Given At The National Science Foundation Regional Conference On Control Theory Conference Board Of The Mathematical Sciences Regional Conference Series In Applied Mathematics
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Some Aspects of the Optimal Control of Distributed Parameter Systems
The applications of the theory of Optimal Control of distributed parameters is an extremely wide field and, although a large number of questions remain open, the whole subject continues to expand very rapidly. The author does not attempt to cover the field but does discuss a number of the more interesting areas of application.
Computational Methods in Optimal Control
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions. 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.
Mathematics of Genetic Diversity
This book draws together some mathematical ideas that are useful in population genetics, concentrating on a few aspects which are both biologically relevant and mathematically interesting.