  The dyadic adaptive control architecture evolved as a solution to the problem
of designing control laws for nonlinear systems with unmatched nonlinearities,
disturbances and uncertainties. A salient feature of this framework is its
ability to work with infinite as well as finite dimensional systems, and with a
wide range of control and adaptive laws. In this paper, we consider the case
where a control law based on the linear quadratic regulator theory is employed
for designing the control law. We benchmark the closed-loop system against
standard linear quadratic control laws as well as those based on the
state-dependent Riccati equation. We pose the problem of designing a part of
the control law as a Nehari problem. We obtain analytical expressions for the
bounds on the sub-optimality of the control law.
