On the design of regulator systems using bounding optimal initial state manifolds

This paper presents a discussion of techniques for designing optimal linear time-invariant regulator systems, which have inaccessible states, and which are based on a quadratic performance functional for the definition of optimality. A definition is given of a suboptimal control vector
\hat{k}
, which has
m
nonzero, constant elements and
n - m
elements defined as zero, and which will provide optimal performance from an
m
-dimensional linear manifold of initial states. An algorithm is given for determining
\hat{k}
for a linear manifold lying between two optimal manifolds and an example illustrates the superiority of these routines for initial-state sets about an optimal manifold.