Direct Methods in Control Problems

Description

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—requiring necessary or other auxiliary conditions—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. Historically not yet fully exploited, direct methods such as finite element, integration and representation methods are developed here in a rather abstract, functional analytic way. 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. Key features: * General theory is developed in a unified way and applied in the control and systems context. * A gap in the literature is filled: While there is a considerable literature on direct method techniques, there is very little coverage of their applications in the control and systems context. * New material is presented, in particular, a treatment of representation methods for stochastic processes involving Lévy processes. * Varied examples throughout represent a valuable pedagogical tool and are also of independent interest to researchers and students. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers. In addition, some of the material is of independent mathematical interest and could be useful in a variety of areas such as numerical analysis and stochastic processes. The work may be used as a textbook for a graduate course or seminar on direct methods in control, requiring a considerable degree of mathematical sophistication and some knowledge of control theory.