The problem of controlling or stabilizing a system of differential
equa tions in the presence of random disturbances is intuitively
appealing and has been a motivating force behind a wide variety of
results grouped loosely together under the heading of "Stochastic
Control." This book is concerned with a special instance of this
general problem, the "Adaptive LQ Regulator," which is a stochastic
control problem of partially observed type that can, in certain
cases, be solved explicitly. We first describe this problem, as it
is the focal point for the entire book, and then describe the
contents of the book. The problem revolves around an uncertain
linear system x(O) = x~ in R", where 0 E {1, ... , N} is a random
variable representing this uncertainty and (Ai' B , C) and xJ are
the coefficient matrices and initial state, respectively, of j j a
linear control system, for eachj = 1, ... , N. A common assumption
is that the mechanism causing this uncertainty is additive noise,
and that conse quently the "controller" has access only to the
observation process y( . ) where y = Cex +~.
General
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