Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years.

The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems.

The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.

Part I. Introduction.- Introductory Remarks.- Historical Perspective.- Outline of Contents.- Part II. Problem Statement.- Deterministic Systems.- Stochastic Systems.- General Problem.- Part III. The Direct Method Approach: Generalities.- General Approach.- Gradient and Integration Methods.- Representation Methods.- Part IV. Gradient and Integration Methods in Control Problems.- Computation of Gradients for ODE Problems.- Computation of Gradients for PDE Problems.- Integration Methods.- Part V. Representation Methods.- Ritz-Galerkin Expansion.- Karhunen-Loeve Expansion.- Lévy Processes.- Bibliography.- Index