On constrained steady-state optimal control: Dynamic KKT controllers

This paper presents a solution to the problem of controlling a general linear time-invariant dynamical system (plant) to a time-varying economically optimal operating point. The plant is characterized by a set of exogenous inputs as an abstraction of time-varying loads and disturbances. The economically optimal operating point is implicitly defined as a solution to a given constrained convex optimization problem, which is related to steady-state operation of the plant. A subset of the plant's states and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem. The proposed control structure, which is proven to solve the considered control problem, is explicitly defined and is based on the dynamic extension of the Karush-Kuhn-Tucker (KKT) optimality conditions for the steady-state related optimization problem.