Infinite Horizon Optimal Control: Deterministic and Stochastic Systems

This book presents a systematic account of the development of deterministic, continuous time, optimal control problems defined on an unbounded time interval, based on work ranging from the early seventies to the present. The authors have strived to present the work in a manner accessible to a broad audience. With this in mind, the first five chapters require, for the most part, a minimal knowledge of mathematical control theory and therefore provide a good introduction to the subject. The remainder of the book requires more sophisticated mathematics. Throughout the book it is possible to distinguish three categories of research. First, the extension of the classical necessary conditions to the various weaker types of optimality (eg. overtaking optimality); secondly, the discussion of various sufficient conditions and verification theorems; and finally, the discussion of existence theorems for the various types of optimality. The common link between these categories is the "Turnpike Property". Once this property is seen to hold, it is possible to begin investigating the above categories.