We consider the problem of designing a feedback controller for a
multivariable nonlinear system that regulates an arbitrary subset of the system
states and inputs to the solution of a constrained optimization problem,
despite parametric modelling uncertainty and time-varying exogenous
disturbances; we term this the optimal steady-state (OSS) control problem. We
derive necessary and sufficient conditions for the existence of an OSS
controller by formulating the OSS control problem as an output regulation
problem wherein the regulation error is unmeasurable. We introduce the notion
of an optimality model, and show that the existence of an optimality model is
sufficient to reduce the OSS control problem to an output regulation problem
with measurable error. This yields a design framework for OSS control that
unifies and extends many existing designs in the literature. We present a
complete and constructive solution of the OSS control problem for the case
where the plant is linear time-invariant with structured parametric
uncertainty, and disturbances are constant in time. We illustrate these results
via an application to optimal frequency control of power networks, and show
that our design procedure recovers several frequency controllers from the
recent literature.