On Constrained Steady-State Regulation: Dynamic KKT Controllers

This technical note presents a solution to the problem of regulating a general nonlinear dynamical system to an 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. The proposed solution is based on a specific dynamic extension of the Karush–Kuhn–Tucker optimality conditions for the steady-state related optimization problem, which is conceptually related to the continuous-time Arrow–Hurwicz–Uzawa algorithm. Furthermore, it can be interpreted as a generalization of the standard output regulation problem with respect to a constant reference signal.