A dominance concept for optimal control with partially unknown initial conditions

The problems considered here have cost
v(x_{o}, u)
, a quadratic in
(x_{o}, u)
, wherex
o
is interpreted as an initial condition and
u
as an unconstrained control variable. The aim is to choose
u
rationally when the only measurement available is the partial linear measurement
y_{o} = Cx_{o}
and when
u
should be desirable for every x
o
consistent with the measurement y
o
. A dominance concept is introduced which facilitates suitable choice of
u
. Properties of such
u
are studied. The results are applied to the standard linear regulator, giving an open-loop control dependent on y
o
, and to the problem of choosing the initial conditions for dynamic compensators.