Optimal control. Basics and beyond

Описание

Preface
Anyone who writes on the subject of control without having faced the
responsibility of practical implementation should be conscious of his presumption, and
the strength of this sense should be at least doubled if he writes on optimal
control. Beautiful theories commonly wither when put to the test, usually
because factors are present which simply had not been envisaged. This is the
reason why the design of practical control systems still has aspects of an art, for
all the science on which it now calls.
Nevertheless, even an art requires guidelines, and it can be claimed that the
proper function of a quest for optimality is just the revelation of fundamental
guidelines. The notion of achieving optimality in systems of the degree of
complexity encountered in practice is a delusion, but the attempt to optimise
idealised systems does generate the fundamental concepts needed for the
enlightened treatment of less ideal cases. This observation then has a corollary:
the theory must be natural and incisive enough that it does generate recognisable
concepts; a theory which ends in an opaque jumble of formulae has served no
purpose.
'Control theory' is now understood not merely in the narrow sense of the
control of mechanisms but in the wider sense of the control of any dynamic
system (e.g. communication, distribution, production, financial, economic), in
general stochastic and imperfectly observed. The text takes this wider view and
so covers general techniques of optimisation (e.g. dynamic programming and the
maximum principle) as well as topics more classically associated with narrow-
sense control theory (e.g. stability, feedback, controllability). There is now a great
deal of standard material in this area, and it is to this which the 'basics'
component of the book provides an introduction. However, while the material
may be standard, the treatment of the section is shaped considerably by
consciousness of the 'beyond'component into which it leads.
There are two pieces of standard theory which impress one as complete: one
is the Pontryagin maximum principle for the optimisation of deterministic
processes; the other is the optimisation of LQG models (a class of stochastic
models with Linear dynamics, Quadratic costs and Gaussian noise). These have
appeared like two islands in a sea of problems for which little more than an ad
hoc treatment was available. However, in recent years the sea-bed has begun to
rise and depths have become shallows, shallows have become bridging dry land.
The class of risk-sensitive models, LEQG models, was introduced, and it was

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