The problem of developing a systematic approach to the design of feed-
back strategies capable of shaping the response of complicated dynamical
control systems illustrates the integration of a wide variety of
mathemat- ical disciplines typical of the modern theory of systems and
control. As a concrete example, one may consider the control of fluid
flow across an airfoil, for which recent experiments indicate the
possibility of delaying the onset of turbulence by controlling viscosity
through thermal actuators located on the airfoil. In general, there are
two approaches to the con- trol of such a complica. ted process, the
development of extremely detailed models of the process followed by the
derivation of a more "dedicated" feed- back law or the development of a
more simple model class followed by the derivation of control laws which
are more robust to unmodelled dynamics and exogeneous disturbances. In
either approach, the two twin themes of approximation and computation
play a significant role in the derivation and implementation of
resulting control laws. And there is no doubt that the
cross-fertilization between these twin themes and control theory will
increase unabated throughout the next decade, not just as an important
component of design and implementation of control laws but also as a
source of new problems in computational mathematics. In this volume, we
present a collection of papers which were deliv- ered at the first
Bozeman Conference on Computation and Control, held at Montana State
University on August 1-11, 1988.
