This book is concerned with a class of discrete-time stochastic control
processes known as controlled Markov processes (CMP's), also known as
Markov decision processes or Markov dynamic programs. Starting in the
mid-1950swith Richard Bellman, many contributions to CMP's have been
made, and applications to engineering, statistics and operations
research, among other areas, have also been developed. The purpose of
this book is to present some recent developments on the theory of
adaptive CMP's, i. e., CMP's that depend on unknown parameters. Thus at
each decision time, the controller or decision-maker must estimate the
true parameter values, and then adapt the control actions to the
estimated values. We do not intend to describe all aspects of stochastic
adaptive control; rather, the selection of material reflects our own
research interests. The prerequisite for this book is a knowledgeof real
analysis and prob- ability theory at the level of, say, Ash (1972) or
Royden (1968), but no previous knowledge of control or decision
processes is required. The pre- sentation, on the other hand, is meant
to beself-contained, in the sensethat whenever a result from analysisor
probability is used, it is usually stated in full and references are
supplied for further discussion, if necessary. Several appendices are
provided for this purpose. The material is divided into six chapters.
Chapter 1 contains the basic definitions about the stochastic control
problems we are interested in; a brief description of some applications
is also provided.
