Feedback Optimizing Linear Quadratic Control

In this paper, we propose a feedback-optimizing linear quadratic control (OLQC) algorithm to regulate a discrete-time linear time-invariant (LTI) system to an equilibrium point that is the solution of an steady-state optimization problem. This is achieved despite the presence of unknown constant exogenous disturbances and without a-priori knowledge of the optimal steady-state set-points, or measurements or explicit estimates of disturbances. We develop the OLQC algorithm by indirectly formulating the residuals of the Karush-Kuhn- Tucker (KKT) optimality conditions associated with the equilibrium optimization into the dynamic performance objective of the LQ controller. The proposed algorithm brings the robustness of feedback to the equilibrium optimization problem thereby allowing the true optimal steady-states to be tracked without explicit knowledge of the exogenous disturbances/set-points.