The Optimal Steady-State Control Problem

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.

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