Complementarity Systems in Constrained Steady-State Optimal Control

This paper presents a solution to the problem of regulating a general nonlinear dynamical system to a time-varying economically optimal operating point. The system 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. The system outputs and the exogenous inputs represent respectively the decision variables and the parameters in the optimization problem. Complementarity systems are employed as building blocks to construct a dynamic controller that solves the considered regulation problem. The complementarity solution arises naturally via a dynamic extension of the Karush-Kuhn-Tucker optimality conditions for the steady-state related optimization problem.