Dynamic Programming Richard Bellman

In the period following World War II, it began to be recognized that there were a large number of interesting and significant activities which could be classified as multistage decision processes. It was soon seen that the mathematical problems that arose in their study stretched the conventional confines of analysis, and required new methods for their successful treatment.

An introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations.

This collection of historically and technically important papers follows a logical line of development from early work in mathematical control theory to studies in adaptive control processes. The book touches upon all the major themes: stability theory, feedback control, time lag, prediction theory, dynamic programming, "bang-bang" control, and maximum principles.

An introduction to a variety of perturbation techniques for ordinary differential equations, this work outlines applications through specific examples. Mathematicians, engineers, and applied scientists will find its exposition entirely accessible.

The purpose of this book is to present some new methods in the treatment of partial differential equations. Some of these methods lead to effective numerical algorithms when combined with the digital computer. Also presented is a useful chapter on Green's functions which generalizes, after an introduction, to new methods of obtaining Green's functions for partial differential operators. Finally some very new material is presented on solving partial differential equations by Adomian's decomposition methodology. This method can yield realistic computable solutions for linear or non­ linear cases even for strong nonlinearities, and also for deterministic or stochastic cases - again even if strong stochasticity is involved. Some interesting examples are discussed here and are to be followed by a book dealing with frontier applications in physics and engineering. In Chapter I, it is shown that a use of positive operators can lead to monotone convergence for various classes of nonlinear partial differential equations. In Chapter II, the utility of conservation technique is shown. These techniques are suggested by physical principles. In Chapter III, it is shown that dyn~mic programming applied to variational problems leads to interesting classes of nonlinear partial differential equations. In Chapter IV, this is investigated in greater detail. In Chapter V, we show. that the use of a transformation suggested by dynamic programming leads to a new method of successive approximations.